KILLED proof of input_KVWxS44Eia.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 49 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (10) TRS for Loop Detection (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxRelTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 9 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 101 ms] (16) typed CpxTrs (17) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (18) CpxWeightedTrs (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxTypedWeightedTrs (21) CompletionProof [UPPER BOUND(ID), 0 ms] (22) CpxTypedWeightedCompleteTrs (23) NarrowingProof [BOTH BOUNDS(ID, ID), 1507 ms] (24) CpxTypedWeightedCompleteTrs (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 1 ms] (26) CpxRNTS (27) InliningProof [UPPER BOUND(ID), 675 ms] (28) CpxRNTS (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxRNTS (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 10 ms] (34) CpxRNTS (35) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (36) CdtProblem (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 1 ms] (38) CdtProblem (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CpxRelTRS (43) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (44) CpxTRS (45) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CpxWeightedTrs (47) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CpxTypedWeightedTrs (49) CompletionProof [UPPER BOUND(ID), 0 ms] (50) CpxTypedWeightedCompleteTrs (51) NarrowingProof [BOTH BOUNDS(ID, ID), 22.0 s] (52) CpxTypedWeightedCompleteTrs (53) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 11 ms] (54) CpxRNTS (55) InliningProof [UPPER BOUND(ID), 1404 ms] (56) CpxRNTS (57) SimplificationProof [BOTH BOUNDS(ID, ID), 15 ms] (58) CpxRNTS (59) CompletionProof [UPPER BOUND(ID), 217 ms] (60) CpxTypedWeightedCompleteTrs (61) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (62) CpxRNTS (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 20 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 24 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms] (102) CdtProblem (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 49 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 32 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 66 ms] (122) CdtProblem (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms] (128) CdtProblem (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 6 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 79 ms] (140) CdtProblem (141) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 86 ms] (146) CdtProblem (147) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 106 ms] (152) CdtProblem (153) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 90 ms] (158) CdtProblem (159) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 124 ms] (164) CdtProblem (165) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 102 ms] (170) CdtProblem (171) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 127 ms] (176) CdtProblem (177) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 130 ms] (182) CdtProblem (183) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 10 ms] (186) CdtProblem (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 149 ms] (188) CdtProblem (189) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 341 ms] (194) CdtProblem (195) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CdtProblem (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 463 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 20 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 201 ms] (204) CdtProblem (205) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 13 ms] (206) CdtProblem (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (208) CdtProblem (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms] (210) CdtProblem (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 23 ms] (212) CdtProblem (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 125 ms] (214) CdtProblem (215) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (216) CdtProblem (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 91 ms] (218) CdtProblem (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 11 ms] (220) CdtProblem (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 112 ms] (222) CdtProblem (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (224) CdtProblem (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 105 ms] (226) CdtProblem (227) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (228) CdtProblem (229) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 113 ms] (230) CdtProblem (231) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (232) CdtProblem (233) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 65 ms] (234) CdtProblem (235) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (236) CdtProblem (237) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 134 ms] (238) CdtProblem (239) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (240) CdtProblem (241) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 100 ms] (242) CdtProblem (243) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (244) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__zeros -> cons(0, zeros) a__U11(tt, V1) -> a__U12(a__isNatList(V1)) a__U12(tt) -> tt a__U21(tt, V1) -> a__U22(a__isNat(V1)) a__U22(tt) -> tt a__U31(tt, V) -> a__U32(a__isNatList(V)) a__U32(tt) -> tt a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2) a__U42(tt, V2) -> a__U43(a__isNatIList(V2)) a__U43(tt) -> tt a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2) a__U52(tt, V2) -> a__U53(a__isNatList(V2)) a__U53(tt) -> tt a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2) a__U62(tt, V2) -> a__U63(a__isNatIList(V2)) a__U63(tt) -> tt a__U71(tt, L) -> s(a__length(mark(L))) a__U81(tt) -> nil a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) a__and(tt, X) -> mark(X) a__isNat(0) -> tt a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) a__isNatIList(zeros) -> tt a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) a__isNatKind(0) -> tt a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(nil) -> tt a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) a__length(nil) -> 0 a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) mark(zeros) -> a__zeros mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1, X2)) -> a__U21(mark(X1), X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(U42(X1, X2)) -> a__U42(mark(X1), X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) mark(U52(X1, X2)) -> a__U52(mark(X1), X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) mark(U62(X1, X2)) -> a__U62(mark(X1), X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1, X2)) -> a__U71(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(X) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X1, X2) -> U11(X1, X2) a__U12(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1, X2) -> U21(X1, X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1, X2) -> U31(X1, X2) a__U32(X) -> U32(X) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__U42(X1, X2) -> U42(X1, X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1, X2, X3) -> U51(X1, X2, X3) a__U52(X1, X2) -> U52(X1, X2) a__U53(X) -> U53(X) a__U61(X1, X2, X3) -> U61(X1, X2, X3) a__U62(X1, X2) -> U62(X1, X2) a__U63(X) -> U63(X) a__U71(X1, X2) -> U71(X1, X2) a__length(X) -> length(X) a__U81(X) -> U81(X) a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) a__take(X1, X2) -> take(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__zeros -> cons(0', zeros) a__U11(tt, V1) -> a__U12(a__isNatList(V1)) a__U12(tt) -> tt a__U21(tt, V1) -> a__U22(a__isNat(V1)) a__U22(tt) -> tt a__U31(tt, V) -> a__U32(a__isNatList(V)) a__U32(tt) -> tt a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2) a__U42(tt, V2) -> a__U43(a__isNatIList(V2)) a__U43(tt) -> tt a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2) a__U52(tt, V2) -> a__U53(a__isNatList(V2)) a__U53(tt) -> tt a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2) a__U62(tt, V2) -> a__U63(a__isNatIList(V2)) a__U63(tt) -> tt a__U71(tt, L) -> s(a__length(mark(L))) a__U81(tt) -> nil a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) a__and(tt, X) -> mark(X) a__isNat(0') -> tt a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) a__isNatIList(zeros) -> tt a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) a__isNatKind(0') -> tt a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(nil) -> tt a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) a__length(nil) -> 0' a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) a__take(0', IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) mark(zeros) -> a__zeros mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1, X2)) -> a__U21(mark(X1), X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(U42(X1, X2)) -> a__U42(mark(X1), X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) mark(U52(X1, X2)) -> a__U52(mark(X1), X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) mark(U62(X1, X2)) -> a__U62(mark(X1), X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1, X2)) -> a__U71(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(X) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0') -> 0' mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X1, X2) -> U11(X1, X2) a__U12(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1, X2) -> U21(X1, X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1, X2) -> U31(X1, X2) a__U32(X) -> U32(X) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__U42(X1, X2) -> U42(X1, X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1, X2, X3) -> U51(X1, X2, X3) a__U52(X1, X2) -> U52(X1, X2) a__U53(X) -> U53(X) a__U61(X1, X2, X3) -> U61(X1, X2, X3) a__U62(X1, X2) -> U62(X1, X2) a__U63(X) -> U63(X) a__U71(X1, X2) -> U71(X1, X2) a__length(X) -> length(X) a__U81(X) -> U81(X) a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) a__take(X1, X2) -> take(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__zeros -> cons(0, zeros) a__U11(tt, V1) -> a__U12(a__isNatList(V1)) a__U12(tt) -> tt a__U21(tt, V1) -> a__U22(a__isNat(V1)) a__U22(tt) -> tt a__U31(tt, V) -> a__U32(a__isNatList(V)) a__U32(tt) -> tt a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2) a__U42(tt, V2) -> a__U43(a__isNatIList(V2)) a__U43(tt) -> tt a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2) a__U52(tt, V2) -> a__U53(a__isNatList(V2)) a__U53(tt) -> tt a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2) a__U62(tt, V2) -> a__U63(a__isNatIList(V2)) a__U63(tt) -> tt a__U71(tt, L) -> s(a__length(mark(L))) a__U81(tt) -> nil a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) a__and(tt, X) -> mark(X) a__isNat(0) -> tt a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) a__isNatIList(zeros) -> tt a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) a__isNatKind(0) -> tt a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(nil) -> tt a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) a__length(nil) -> 0 a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) mark(zeros) -> a__zeros mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1, X2)) -> a__U21(mark(X1), X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) mark(U42(X1, X2)) -> a__U42(mark(X1), X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) mark(U52(X1, X2)) -> a__U52(mark(X1), X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) mark(U62(X1, X2)) -> a__U62(mark(X1), X2) mark(U63(X)) -> a__U63(mark(X)) mark(U71(X1, X2)) -> a__U71(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(X) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X1, X2) -> U11(X1, X2) a__U12(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1, X2) -> U21(X1, X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1, X2) -> U31(X1, X2) a__U32(X) -> U32(X) a__U41(X1, X2, X3) -> U41(X1, X2, X3) a__U42(X1, X2) -> U42(X1, X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1, X2, X3) -> U51(X1, X2, X3) a__U52(X1, X2) -> U52(X1, X2) a__U53(X) -> U53(X) a__U61(X1, X2, X3) -> U61(X1, X2, X3) a__U62(X1, X2) -> U62(X1, X2) a__U63(X) -> U63(X) a__U71(X1, X2) -> U71(X1, X2) a__length(X) -> length(X) a__U81(X) -> U81(X) a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) a__take(X1, X2) -> take(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0)) A__U11(z0, z1) -> c3 A__U12(tt) -> c4 A__U12(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0)) A__U31(z0, z1) -> c11 A__U32(tt) -> c12 A__U32(z0) -> c13 A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U41(z0, z1, z2) -> c15 A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U42(z0, z1) -> c17 A__U43(tt) -> c18 A__U43(z0) -> c19 A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U51(z0, z1, z2) -> c21 A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0)) A__U52(z0, z1) -> c23 A__U53(tt) -> c24 A__U53(z0) -> c25 A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(z0, z1, z2) -> c27 A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U62(z0, z1) -> c29 A__U63(tt) -> c30 A__U63(z0) -> c31 A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U71(z0, z1) -> c33 A__U81(tt) -> c34 A__U81(z0) -> c35 A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__U91(z0, z1, z2, z3) -> c37 A__AND(tt, z0) -> c38(MARK(z0)) A__AND(z0, z1) -> c39 A__ISNAT(0) -> c40 A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c43 A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(zeros) -> c45 A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c47 A__ISNATILISTKIND(nil) -> c48 A__ISNATILISTKIND(zeros) -> c49 A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(z0) -> c52 A__ISNATKIND(0) -> c53 A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c56 A__ISNATLIST(nil) -> c57 A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(z0) -> c60 A__LENGTH(nil) -> c61 A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__LENGTH(z0) -> c63 A__TAKE(0, z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c66 MARK(zeros) -> c67(A__ZEROS) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(0) -> c96 MARK(tt) -> c97 MARK(s(z0)) -> c98(MARK(z0)) MARK(nil) -> c99 S tuples: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0)) A__U11(z0, z1) -> c3 A__U12(tt) -> c4 A__U12(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0)) A__U31(z0, z1) -> c11 A__U32(tt) -> c12 A__U32(z0) -> c13 A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U41(z0, z1, z2) -> c15 A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U42(z0, z1) -> c17 A__U43(tt) -> c18 A__U43(z0) -> c19 A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U51(z0, z1, z2) -> c21 A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0)) A__U52(z0, z1) -> c23 A__U53(tt) -> c24 A__U53(z0) -> c25 A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(z0, z1, z2) -> c27 A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U62(z0, z1) -> c29 A__U63(tt) -> c30 A__U63(z0) -> c31 A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U71(z0, z1) -> c33 A__U81(tt) -> c34 A__U81(z0) -> c35 A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__U91(z0, z1, z2, z3) -> c37 A__AND(tt, z0) -> c38(MARK(z0)) A__AND(z0, z1) -> c39 A__ISNAT(0) -> c40 A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c43 A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(zeros) -> c45 A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c47 A__ISNATILISTKIND(nil) -> c48 A__ISNATILISTKIND(zeros) -> c49 A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(z0) -> c52 A__ISNATKIND(0) -> c53 A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c56 A__ISNATLIST(nil) -> c57 A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(z0) -> c60 A__LENGTH(nil) -> c61 A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__LENGTH(z0) -> c63 A__TAKE(0, z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c66 MARK(zeros) -> c67(A__ZEROS) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(0) -> c96 MARK(tt) -> c97 MARK(s(z0)) -> c98(MARK(z0)) MARK(nil) -> c99 K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__ZEROS, A__U11_2, A__U12_1, A__U21_2, A__U22_1, A__U31_2, A__U32_1, A__U41_3, A__U42_2, A__U43_1, A__U51_3, A__U52_2, A__U53_1, A__U61_3, A__U62_2, A__U63_1, A__U71_2, A__U81_1, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c, c1, c2_2, c3, c4, c5, c6_2, c7, c8, c9, c10_2, c11, c12, c13, c14_2, c15, c16_2, c17, c18, c19, c20_2, c21, c22_2, c23, c24, c25, c26_2, c27, c28_2, c29, c30, c31, c32_2, c33, c34, c35, c36_1, c37, c38_1, c39, c40, c41_2, c42_2, c43, c44_2, c45, c46_3, c47, c48, c49, c50_2, c51_2, c52, c53, c54_1, c55_1, c56, c57, c58_3, c59_3, c60, c61, c62_4, c63, c64_3, c65_4, c66, c67_1, c68_2, c69_2, c70_1, c71_2, c72_2, c73_1, c74_2, c75_2, c76_2, c77_2, c78_2, c79_1, c80_2, c81_2, c82_2, c83_2, c84_2, c85_2, c86_2, c87_2, c88_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c96, c97, c98_1, c99 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0)) A__U11(z0, z1) -> c3 A__U12(tt) -> c4 A__U12(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0)) A__U31(z0, z1) -> c11 A__U32(tt) -> c12 A__U32(z0) -> c13 A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U41(z0, z1, z2) -> c15 A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U42(z0, z1) -> c17 A__U43(tt) -> c18 A__U43(z0) -> c19 A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U51(z0, z1, z2) -> c21 A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0)) A__U52(z0, z1) -> c23 A__U53(tt) -> c24 A__U53(z0) -> c25 A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(z0, z1, z2) -> c27 A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U62(z0, z1) -> c29 A__U63(tt) -> c30 A__U63(z0) -> c31 A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U71(z0, z1) -> c33 A__U81(tt) -> c34 A__U81(z0) -> c35 A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__U91(z0, z1, z2, z3) -> c37 A__AND(tt, z0) -> c38(MARK(z0)) A__AND(z0, z1) -> c39 A__ISNAT(0) -> c40 A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c43 A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(zeros) -> c45 A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c47 A__ISNATILISTKIND(nil) -> c48 A__ISNATILISTKIND(zeros) -> c49 A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(z0) -> c52 A__ISNATKIND(0) -> c53 A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c56 A__ISNATLIST(nil) -> c57 A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(z0) -> c60 A__LENGTH(nil) -> c61 A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__LENGTH(z0) -> c63 A__TAKE(0, z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c66 MARK(zeros) -> c67(A__ZEROS) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(0) -> c96 MARK(tt) -> c97 MARK(s(z0)) -> c98(MARK(z0)) MARK(nil) -> c99 The (relative) TRS S consists of the following rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Rewrite Strategy: INNERMOST ---------------------------------------- (9) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (10) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0)) A__U11(z0, z1) -> c3 A__U12(tt) -> c4 A__U12(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0)) A__U31(z0, z1) -> c11 A__U32(tt) -> c12 A__U32(z0) -> c13 A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U41(z0, z1, z2) -> c15 A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U42(z0, z1) -> c17 A__U43(tt) -> c18 A__U43(z0) -> c19 A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U51(z0, z1, z2) -> c21 A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0)) A__U52(z0, z1) -> c23 A__U53(tt) -> c24 A__U53(z0) -> c25 A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(z0, z1, z2) -> c27 A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U62(z0, z1) -> c29 A__U63(tt) -> c30 A__U63(z0) -> c31 A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U71(z0, z1) -> c33 A__U81(tt) -> c34 A__U81(z0) -> c35 A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__U91(z0, z1, z2, z3) -> c37 A__AND(tt, z0) -> c38(MARK(z0)) A__AND(z0, z1) -> c39 A__ISNAT(0) -> c40 A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c43 A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(zeros) -> c45 A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c47 A__ISNATILISTKIND(nil) -> c48 A__ISNATILISTKIND(zeros) -> c49 A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(z0) -> c52 A__ISNATKIND(0) -> c53 A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c56 A__ISNATLIST(nil) -> c57 A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(z0) -> c60 A__LENGTH(nil) -> c61 A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__LENGTH(z0) -> c63 A__TAKE(0, z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c66 MARK(zeros) -> c67(A__ZEROS) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(0) -> c96 MARK(tt) -> c97 MARK(s(z0)) -> c98(MARK(z0)) MARK(nil) -> c99 The (relative) TRS S consists of the following rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Rewrite Strategy: INNERMOST ---------------------------------------- (11) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (12) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0)) A__U11(z0, z1) -> c3 A__U12(tt) -> c4 A__U12(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0)) A__U31(z0, z1) -> c11 A__U32(tt) -> c12 A__U32(z0) -> c13 A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U41(z0, z1, z2) -> c15 A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U42(z0, z1) -> c17 A__U43(tt) -> c18 A__U43(z0) -> c19 A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U51(z0, z1, z2) -> c21 A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0)) A__U52(z0, z1) -> c23 A__U53(tt) -> c24 A__U53(z0) -> c25 A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(z0, z1, z2) -> c27 A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U62(z0, z1) -> c29 A__U63(tt) -> c30 A__U63(z0) -> c31 A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U71(z0, z1) -> c33 A__U81(tt) -> c34 A__U81(z0) -> c35 A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__U91(z0, z1, z2, z3) -> c37 A__AND(tt, z0) -> c38(MARK(z0)) A__AND(z0, z1) -> c39 A__ISNAT(0') -> c40 A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c43 A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(zeros) -> c45 A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c47 A__ISNATILISTKIND(nil) -> c48 A__ISNATILISTKIND(zeros) -> c49 A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(z0) -> c52 A__ISNATKIND(0') -> c53 A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c56 A__ISNATLIST(nil) -> c57 A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(z0) -> c60 A__LENGTH(nil) -> c61 A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__LENGTH(z0) -> c63 A__TAKE(0', z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c66 MARK(zeros) -> c67(A__ZEROS) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(0') -> c96 MARK(tt) -> c97 MARK(s(z0)) -> c98(MARK(z0)) MARK(nil) -> c99 The (relative) TRS S consists of the following rules: a__zeros -> cons(0', zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0') -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0') -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0' a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0', z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Rewrite Strategy: INNERMOST ---------------------------------------- (13) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0)) A__U11(z0, z1) -> c3 A__U12(tt) -> c4 A__U12(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0)) A__U31(z0, z1) -> c11 A__U32(tt) -> c12 A__U32(z0) -> c13 A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U41(z0, z1, z2) -> c15 A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U42(z0, z1) -> c17 A__U43(tt) -> c18 A__U43(z0) -> c19 A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U51(z0, z1, z2) -> c21 A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0)) A__U52(z0, z1) -> c23 A__U53(tt) -> c24 A__U53(z0) -> c25 A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(z0, z1, z2) -> c27 A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U62(z0, z1) -> c29 A__U63(tt) -> c30 A__U63(z0) -> c31 A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U71(z0, z1) -> c33 A__U81(tt) -> c34 A__U81(z0) -> c35 A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__U91(z0, z1, z2, z3) -> c37 A__AND(tt, z0) -> c38(MARK(z0)) A__AND(z0, z1) -> c39 A__ISNAT(0') -> c40 A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c43 A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(zeros) -> c45 A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c47 A__ISNATILISTKIND(nil) -> c48 A__ISNATILISTKIND(zeros) -> c49 A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(z0) -> c52 A__ISNATKIND(0') -> c53 A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c56 A__ISNATLIST(nil) -> c57 A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(z0) -> c60 A__LENGTH(nil) -> c61 A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__LENGTH(z0) -> c63 A__TAKE(0', z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c66 MARK(zeros) -> c67(A__ZEROS) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(0') -> c96 MARK(tt) -> c97 MARK(s(z0)) -> c98(MARK(z0)) MARK(nil) -> c99 a__zeros -> cons(0', zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0') -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0') -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0' a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0', z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Types: A__ZEROS :: c:c1 c :: c:c1 c1 :: c:c1 A__U11 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c2:c3 tt :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c2 :: c4:c5 -> c57:c58:c59:c60 -> c2:c3 A__U12 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c4:c5 a__isNatList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 A__ISNATLIST :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c57:c58:c59:c60 c3 :: c2:c3 c4 :: c4:c5 c5 :: c4:c5 A__U21 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c6:c7 c6 :: c8:c9 -> c40:c41:c42:c43 -> c6:c7 A__U22 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c8:c9 a__isNat :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 A__ISNAT :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c40:c41:c42:c43 c7 :: c6:c7 c8 :: c8:c9 c9 :: c8:c9 A__U31 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c10:c11 c10 :: c12:c13 -> c57:c58:c59:c60 -> c10:c11 A__U32 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c12:c13 c11 :: c10:c11 c12 :: c12:c13 c13 :: c12:c13 A__U41 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c14:c15 c14 :: c16:c17 -> c40:c41:c42:c43 -> c14:c15 A__U42 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c16:c17 c15 :: c14:c15 c16 :: c18:c19 -> c44:c45:c46:c47 -> c16:c17 A__U43 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c18:c19 a__isNatIList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 A__ISNATILIST :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c44:c45:c46:c47 c17 :: c16:c17 c18 :: c18:c19 c19 :: c18:c19 A__U51 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c20:c21 c20 :: c22:c23 -> c40:c41:c42:c43 -> c20:c21 A__U52 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c22:c23 c21 :: c20:c21 c22 :: c24:c25 -> c57:c58:c59:c60 -> c22:c23 A__U53 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c24:c25 c23 :: c22:c23 c24 :: c24:c25 c25 :: c24:c25 A__U61 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c26:c27 c26 :: c28:c29 -> c40:c41:c42:c43 -> c26:c27 A__U62 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c28:c29 c27 :: c26:c27 c28 :: c30:c31 -> c44:c45:c46:c47 -> c28:c29 A__U63 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c30:c31 c29 :: c28:c29 c30 :: c30:c31 c31 :: c30:c31 A__U71 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c32:c33 c32 :: c61:c62:c63 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c32:c33 A__LENGTH :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c61:c62:c63 mark :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 MARK :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c33 :: c32:c33 A__U81 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c34:c35 c34 :: c34:c35 c35 :: c34:c35 A__U91 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c36:c37 c36 :: c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c36:c37 c37 :: c36:c37 A__AND :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c38:c39 c38 :: c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c38:c39 c39 :: c38:c39 0' :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c40 :: c40:c41:c42:c43 length :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c41 :: c2:c3 -> c48:c49:c50:c51:c52 -> c40:c41:c42:c43 a__isNatIListKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 A__ISNATILISTKIND :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c48:c49:c50:c51:c52 s :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c42 :: c6:c7 -> c53:c54:c55:c56 -> c40:c41:c42:c43 a__isNatKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 A__ISNATKIND :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c53:c54:c55:c56 c43 :: c40:c41:c42:c43 c44 :: c10:c11 -> c48:c49:c50:c51:c52 -> c44:c45:c46:c47 zeros :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c45 :: c44:c45:c46:c47 cons :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c46 :: c14:c15 -> c38:c39 -> c53:c54:c55:c56 -> c44:c45:c46:c47 a__and :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatIListKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c47 :: c44:c45:c46:c47 nil :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c48 :: c48:c49:c50:c51:c52 c49 :: c48:c49:c50:c51:c52 c50 :: c38:c39 -> c53:c54:c55:c56 -> c48:c49:c50:c51:c52 take :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c51 :: c38:c39 -> c53:c54:c55:c56 -> c48:c49:c50:c51:c52 c52 :: c48:c49:c50:c51:c52 c53 :: c53:c54:c55:c56 c54 :: c48:c49:c50:c51:c52 -> c53:c54:c55:c56 c55 :: c53:c54:c55:c56 -> c53:c54:c55:c56 c56 :: c53:c54:c55:c56 c57 :: c57:c58:c59:c60 c58 :: c20:c21 -> c38:c39 -> c53:c54:c55:c56 -> c57:c58:c59:c60 c59 :: c26:c27 -> c38:c39 -> c53:c54:c55:c56 -> c57:c58:c59:c60 c60 :: c57:c58:c59:c60 c61 :: c61:c62:c63 c62 :: c32:c33 -> c38:c39 -> c38:c39 -> c57:c58:c59:c60 -> c61:c62:c63 and :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNat :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c63 :: c61:c62:c63 A__TAKE :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c64:c65:c66 c64 :: c34:c35 -> c38:c39 -> c44:c45:c46:c47 -> c64:c65:c66 c65 :: c36:c37 -> c38:c39 -> c38:c39 -> c44:c45:c46:c47 -> c64:c65:c66 c66 :: c64:c65:c66 c67 :: c:c1 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U11 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c68 :: c2:c3 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U12 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c69 :: c4:c5 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 isNatList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c70 :: c57:c58:c59:c60 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U21 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c71 :: c6:c7 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U22 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c72 :: c8:c9 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c73 :: c40:c41:c42:c43 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U31 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c74 :: c10:c11 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U32 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c75 :: c12:c13 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U41 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c76 :: c14:c15 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U42 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c77 :: c16:c17 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U43 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c78 :: c18:c19 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 isNatIList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c79 :: c44:c45:c46:c47 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U51 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c80 :: c20:c21 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U52 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c81 :: c22:c23 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U53 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c82 :: c24:c25 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U61 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c83 :: c26:c27 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U62 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c84 :: c28:c29 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U63 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c85 :: c30:c31 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U71 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c86 :: c32:c33 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c87 :: c61:c62:c63 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U81 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c88 :: c34:c35 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U91 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c89 :: c36:c37 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c90 :: c64:c65:c66 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c91 :: c64:c65:c66 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c92 :: c38:c39 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c93 :: c48:c49:c50:c51:c52 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c94 :: c53:c54:c55:c56 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c95 :: c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c96 :: c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c97 :: c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c98 :: c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c99 :: c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 a__zeros :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U11 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U12 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U21 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U22 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U31 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U32 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U41 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U42 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U43 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U51 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U52 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U53 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U61 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U62 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U63 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U71 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__length :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U81 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U91 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__take :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 hole_c:c11_100 :: c:c1 hole_c2:c32_100 :: c2:c3 hole_tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U913_100 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 hole_c4:c54_100 :: c4:c5 hole_c57:c58:c59:c605_100 :: c57:c58:c59:c60 hole_c6:c76_100 :: c6:c7 hole_c8:c97_100 :: c8:c9 hole_c40:c41:c42:c438_100 :: c40:c41:c42:c43 hole_c10:c119_100 :: c10:c11 hole_c12:c1310_100 :: c12:c13 hole_c14:c1511_100 :: c14:c15 hole_c16:c1712_100 :: c16:c17 hole_c18:c1913_100 :: c18:c19 hole_c44:c45:c46:c4714_100 :: c44:c45:c46:c47 hole_c20:c2115_100 :: c20:c21 hole_c22:c2316_100 :: c22:c23 hole_c24:c2517_100 :: c24:c25 hole_c26:c2718_100 :: c26:c27 hole_c28:c2919_100 :: c28:c29 hole_c30:c3120_100 :: c30:c31 hole_c32:c3321_100 :: c32:c33 hole_c61:c62:c6322_100 :: c61:c62:c63 hole_c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c9923_100 :: c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 hole_c34:c3524_100 :: c34:c35 hole_c36:c3725_100 :: c36:c37 hole_c38:c3926_100 :: c38:c39 hole_c48:c49:c50:c51:c5227_100 :: c48:c49:c50:c51:c52 hole_c53:c54:c55:c5628_100 :: c53:c54:c55:c56 hole_c64:c65:c6629_100 :: c64:c65:c66 gen_tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U9130_100 :: Nat -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 gen_c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c9931_100 :: Nat -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 gen_c53:c54:c55:c5632_100 :: Nat -> c53:c54:c55:c56 ---------------------------------------- (15) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__U11, a__isNatList, A__ISNATLIST, A__U21, a__isNat, A__ISNAT, A__U31, A__U41, A__U42, a__isNatIList, A__ISNATILIST, A__U51, A__U52, A__U61, A__U62, A__U71, A__LENGTH, mark, MARK, A__U91, A__AND, a__isNatIListKind, A__ISNATILISTKIND, a__isNatKind, A__ISNATKIND, a__and, a__U11, a__U21, a__U31, a__U41, a__U42, a__U51, a__U52, a__U61, a__U62, a__U71, a__length, a__U91 They will be analysed ascendingly in the following order: a__isNatList < A__U11 A__U11 = A__ISNATLIST A__U11 = A__U21 A__U11 = A__ISNAT A__U11 = A__U31 A__U11 = A__U41 A__U11 = A__U42 A__U11 = A__ISNATILIST A__U11 = A__U51 A__U11 = A__U52 A__U11 = A__U61 A__U11 = A__U62 A__U11 = A__U71 A__U11 = A__LENGTH A__U11 = MARK A__U11 = A__U91 A__U11 = A__AND A__U11 = A__ISNATILISTKIND A__U11 = A__ISNATKIND a__isNatList = a__isNat a__isNatList < A__U31 a__isNatList = a__isNatIList a__isNatList < A__U52 a__isNatList < A__LENGTH a__isNatList = mark a__isNatList = a__isNatIListKind a__isNatList = a__isNatKind a__isNatList = a__and a__isNatList = a__U11 a__isNatList = a__U21 a__isNatList = a__U31 a__isNatList = a__U41 a__isNatList = a__U42 a__isNatList = a__U51 a__isNatList = a__U52 a__isNatList = a__U61 a__isNatList = a__U62 a__isNatList = a__U71 a__isNatList = a__length a__isNatList = a__U91 A__ISNATLIST = A__U21 A__ISNATLIST = A__ISNAT A__ISNATLIST = A__U31 A__ISNATLIST = A__U41 A__ISNATLIST = A__U42 A__ISNATLIST = A__ISNATILIST A__ISNATLIST = A__U51 A__ISNATLIST = A__U52 A__ISNATLIST = A__U61 A__ISNATLIST = A__U62 A__ISNATLIST = A__U71 A__ISNATLIST = A__LENGTH A__ISNATLIST = MARK A__ISNATLIST = A__U91 A__ISNATLIST = A__AND A__ISNATLIST = A__ISNATILISTKIND a__isNatKind < A__ISNATLIST A__ISNATLIST = A__ISNATKIND a__and < A__ISNATLIST a__isNat < A__U21 A__U21 = A__ISNAT A__U21 = A__U31 A__U21 = A__U41 A__U21 = A__U42 A__U21 = A__ISNATILIST A__U21 = A__U51 A__U21 = A__U52 A__U21 = A__U61 A__U21 = A__U62 A__U21 = A__U71 A__U21 = A__LENGTH A__U21 = MARK A__U21 = A__U91 A__U21 = A__AND A__U21 = A__ISNATILISTKIND A__U21 = A__ISNATKIND a__isNat < A__U41 a__isNat = a__isNatIList a__isNat < A__U51 a__isNat < A__U61 a__isNat = mark a__isNat = a__isNatIListKind a__isNat = a__isNatKind a__isNat = a__and a__isNat = a__U11 a__isNat = a__U21 a__isNat = a__U31 a__isNat = a__U41 a__isNat = a__U42 a__isNat = a__U51 a__isNat = a__U52 a__isNat = a__U61 a__isNat = a__U62 a__isNat = a__U71 a__isNat = a__length a__isNat = a__U91 A__ISNAT = A__U31 A__ISNAT = A__U41 A__ISNAT = A__U42 A__ISNAT = A__ISNATILIST A__ISNAT = A__U51 A__ISNAT = A__U52 A__ISNAT = A__U61 A__ISNAT = A__U62 A__ISNAT = A__U71 A__ISNAT = A__LENGTH A__ISNAT = MARK A__ISNAT = A__U91 A__ISNAT = A__AND a__isNatIListKind < A__ISNAT A__ISNAT = A__ISNATILISTKIND a__isNatKind < A__ISNAT A__ISNAT = A__ISNATKIND A__U31 = A__U41 A__U31 = A__U42 A__U31 = A__ISNATILIST A__U31 = A__U51 A__U31 = A__U52 A__U31 = A__U61 A__U31 = A__U62 A__U31 = A__U71 A__U31 = A__LENGTH A__U31 = MARK A__U31 = A__U91 A__U31 = A__AND A__U31 = A__ISNATILISTKIND A__U31 = A__ISNATKIND A__U41 = A__U42 A__U41 = A__ISNATILIST A__U41 = A__U51 A__U41 = A__U52 A__U41 = A__U61 A__U41 = A__U62 A__U41 = A__U71 A__U41 = A__LENGTH A__U41 = MARK A__U41 = A__U91 A__U41 = A__AND A__U41 = A__ISNATILISTKIND A__U41 = A__ISNATKIND a__isNatIList < A__U42 A__U42 = A__ISNATILIST A__U42 = A__U51 A__U42 = A__U52 A__U42 = A__U61 A__U42 = A__U62 A__U42 = A__U71 A__U42 = A__LENGTH A__U42 = MARK A__U42 = A__U91 A__U42 = A__AND A__U42 = A__ISNATILISTKIND A__U42 = A__ISNATKIND a__isNatIList < A__U62 a__isNatIList = mark a__isNatIList < MARK a__isNatIList = a__isNatIListKind a__isNatIList = a__isNatKind a__isNatIList = a__and a__isNatIList = a__U11 a__isNatIList = a__U21 a__isNatIList = a__U31 a__isNatIList = a__U41 a__isNatIList = a__U42 a__isNatIList = a__U51 a__isNatIList = a__U52 a__isNatIList = a__U61 a__isNatIList = a__U62 a__isNatIList = a__U71 a__isNatIList = a__length a__isNatIList = a__U91 A__ISNATILIST = A__U51 A__ISNATILIST = A__U52 A__ISNATILIST = A__U61 A__ISNATILIST = A__U62 A__ISNATILIST = A__U71 A__ISNATILIST = A__LENGTH A__ISNATILIST = MARK A__ISNATILIST = A__U91 A__ISNATILIST = A__AND a__isNatIListKind < A__ISNATILIST A__ISNATILIST = A__ISNATILISTKIND a__isNatKind < A__ISNATILIST A__ISNATILIST = A__ISNATKIND a__and < A__ISNATILIST A__U51 = A__U52 A__U51 = A__U61 A__U51 = A__U62 A__U51 = A__U71 A__U51 = A__LENGTH A__U51 = MARK A__U51 = A__U91 A__U51 = A__AND A__U51 = A__ISNATILISTKIND A__U51 = A__ISNATKIND A__U52 = A__U61 A__U52 = A__U62 A__U52 = A__U71 A__U52 = A__LENGTH A__U52 = MARK A__U52 = A__U91 A__U52 = A__AND A__U52 = A__ISNATILISTKIND A__U52 = A__ISNATKIND A__U61 = A__U62 A__U61 = A__U71 A__U61 = A__LENGTH A__U61 = MARK A__U61 = A__U91 A__U61 = A__AND A__U61 = A__ISNATILISTKIND A__U61 = A__ISNATKIND A__U62 = A__U71 A__U62 = A__LENGTH A__U62 = MARK A__U62 = A__U91 A__U62 = A__AND A__U62 = A__ISNATILISTKIND A__U62 = A__ISNATKIND A__U71 = A__LENGTH mark < A__U71 A__U71 = MARK A__U71 = A__U91 A__U71 = A__AND A__U71 = A__ISNATILISTKIND A__U71 = A__ISNATKIND A__LENGTH = MARK A__LENGTH = A__U91 A__LENGTH = A__AND A__LENGTH = A__ISNATILISTKIND A__LENGTH = A__ISNATKIND a__and < A__LENGTH mark < MARK mark = a__isNatIListKind mark = a__isNatKind mark = a__and mark = a__U11 mark = a__U21 mark = a__U31 mark = a__U41 mark = a__U42 mark = a__U51 mark = a__U52 mark = a__U61 mark = a__U62 mark = a__U71 mark = a__length mark = a__U91 MARK = A__U91 MARK = A__AND MARK = A__ISNATILISTKIND MARK = A__ISNATKIND a__and < MARK A__U91 = A__AND A__U91 = A__ISNATILISTKIND A__U91 = A__ISNATKIND A__AND = A__ISNATILISTKIND A__AND = A__ISNATKIND a__isNatIListKind = a__isNatKind a__isNatIListKind = a__and a__isNatIListKind = a__U11 a__isNatIListKind = a__U21 a__isNatIListKind = a__U31 a__isNatIListKind = a__U41 a__isNatIListKind = a__U42 a__isNatIListKind = a__U51 a__isNatIListKind = a__U52 a__isNatIListKind = a__U61 a__isNatIListKind = a__U62 a__isNatIListKind = a__U71 a__isNatIListKind = a__length a__isNatIListKind = a__U91 a__isNatKind < A__ISNATILISTKIND A__ISNATILISTKIND = A__ISNATKIND a__isNatKind = a__and a__isNatKind = a__U11 a__isNatKind = a__U21 a__isNatKind = a__U31 a__isNatKind = a__U41 a__isNatKind = a__U42 a__isNatKind = a__U51 a__isNatKind = a__U52 a__isNatKind = a__U61 a__isNatKind = a__U62 a__isNatKind = a__U71 a__isNatKind = a__length a__isNatKind = a__U91 a__and = a__U11 a__and = a__U21 a__and = a__U31 a__and = a__U41 a__and = a__U42 a__and = a__U51 a__and = a__U52 a__and = a__U61 a__and = a__U62 a__and = a__U71 a__and = a__length a__and = a__U91 a__U11 = a__U21 a__U11 = a__U31 a__U11 = a__U41 a__U11 = a__U42 a__U11 = a__U51 a__U11 = a__U52 a__U11 = a__U61 a__U11 = a__U62 a__U11 = a__U71 a__U11 = a__length a__U11 = a__U91 a__U21 = a__U31 a__U21 = a__U41 a__U21 = a__U42 a__U21 = a__U51 a__U21 = a__U52 a__U21 = a__U61 a__U21 = a__U62 a__U21 = a__U71 a__U21 = a__length a__U21 = a__U91 a__U31 = a__U41 a__U31 = a__U42 a__U31 = a__U51 a__U31 = a__U52 a__U31 = a__U61 a__U31 = a__U62 a__U31 = a__U71 a__U31 = a__length a__U31 = a__U91 a__U41 = a__U42 a__U41 = a__U51 a__U41 = a__U52 a__U41 = a__U61 a__U41 = a__U62 a__U41 = a__U71 a__U41 = a__length a__U41 = a__U91 a__U42 = a__U51 a__U42 = a__U52 a__U42 = a__U61 a__U42 = a__U62 a__U42 = a__U71 a__U42 = a__length a__U42 = a__U91 a__U51 = a__U52 a__U51 = a__U61 a__U51 = a__U62 a__U51 = a__U71 a__U51 = a__length a__U51 = a__U91 a__U52 = a__U61 a__U52 = a__U62 a__U52 = a__U71 a__U52 = a__length a__U52 = a__U91 a__U61 = a__U62 a__U61 = a__U71 a__U61 = a__length a__U61 = a__U91 a__U62 = a__U71 a__U62 = a__length a__U62 = a__U91 a__U71 = a__length a__U71 = a__U91 a__length = a__U91 ---------------------------------------- (16) Obligation: Innermost TRS: Rules: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0)) A__U11(z0, z1) -> c3 A__U12(tt) -> c4 A__U12(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0)) A__U31(z0, z1) -> c11 A__U32(tt) -> c12 A__U32(z0) -> c13 A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U41(z0, z1, z2) -> c15 A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U42(z0, z1) -> c17 A__U43(tt) -> c18 A__U43(z0) -> c19 A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U51(z0, z1, z2) -> c21 A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0)) A__U52(z0, z1) -> c23 A__U53(tt) -> c24 A__U53(z0) -> c25 A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(z0, z1, z2) -> c27 A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U62(z0, z1) -> c29 A__U63(tt) -> c30 A__U63(z0) -> c31 A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U71(z0, z1) -> c33 A__U81(tt) -> c34 A__U81(z0) -> c35 A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__U91(z0, z1, z2, z3) -> c37 A__AND(tt, z0) -> c38(MARK(z0)) A__AND(z0, z1) -> c39 A__ISNAT(0') -> c40 A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c43 A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(zeros) -> c45 A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c47 A__ISNATILISTKIND(nil) -> c48 A__ISNATILISTKIND(zeros) -> c49 A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(z0) -> c52 A__ISNATKIND(0') -> c53 A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c56 A__ISNATLIST(nil) -> c57 A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(z0) -> c60 A__LENGTH(nil) -> c61 A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__LENGTH(z0) -> c63 A__TAKE(0', z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c66 MARK(zeros) -> c67(A__ZEROS) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(0') -> c96 MARK(tt) -> c97 MARK(s(z0)) -> c98(MARK(z0)) MARK(nil) -> c99 a__zeros -> cons(0', zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0') -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0') -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0' a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0', z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Types: A__ZEROS :: c:c1 c :: c:c1 c1 :: c:c1 A__U11 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c2:c3 tt :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c2 :: c4:c5 -> c57:c58:c59:c60 -> c2:c3 A__U12 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c4:c5 a__isNatList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 A__ISNATLIST :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c57:c58:c59:c60 c3 :: c2:c3 c4 :: c4:c5 c5 :: c4:c5 A__U21 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c6:c7 c6 :: c8:c9 -> c40:c41:c42:c43 -> c6:c7 A__U22 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c8:c9 a__isNat :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 A__ISNAT :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c40:c41:c42:c43 c7 :: c6:c7 c8 :: c8:c9 c9 :: c8:c9 A__U31 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c10:c11 c10 :: c12:c13 -> c57:c58:c59:c60 -> c10:c11 A__U32 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c12:c13 c11 :: c10:c11 c12 :: c12:c13 c13 :: c12:c13 A__U41 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c14:c15 c14 :: c16:c17 -> c40:c41:c42:c43 -> c14:c15 A__U42 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c16:c17 c15 :: c14:c15 c16 :: c18:c19 -> c44:c45:c46:c47 -> c16:c17 A__U43 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c18:c19 a__isNatIList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 A__ISNATILIST :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c44:c45:c46:c47 c17 :: c16:c17 c18 :: c18:c19 c19 :: c18:c19 A__U51 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c20:c21 c20 :: c22:c23 -> c40:c41:c42:c43 -> c20:c21 A__U52 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c22:c23 c21 :: c20:c21 c22 :: c24:c25 -> c57:c58:c59:c60 -> c22:c23 A__U53 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c24:c25 c23 :: c22:c23 c24 :: c24:c25 c25 :: c24:c25 A__U61 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c26:c27 c26 :: c28:c29 -> c40:c41:c42:c43 -> c26:c27 A__U62 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c28:c29 c27 :: c26:c27 c28 :: c30:c31 -> c44:c45:c46:c47 -> c28:c29 A__U63 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c30:c31 c29 :: c28:c29 c30 :: c30:c31 c31 :: c30:c31 A__U71 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c32:c33 c32 :: c61:c62:c63 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c32:c33 A__LENGTH :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c61:c62:c63 mark :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 MARK :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c33 :: c32:c33 A__U81 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c34:c35 c34 :: c34:c35 c35 :: c34:c35 A__U91 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c36:c37 c36 :: c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c36:c37 c37 :: c36:c37 A__AND :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c38:c39 c38 :: c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c38:c39 c39 :: c38:c39 0' :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c40 :: c40:c41:c42:c43 length :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c41 :: c2:c3 -> c48:c49:c50:c51:c52 -> c40:c41:c42:c43 a__isNatIListKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 A__ISNATILISTKIND :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c48:c49:c50:c51:c52 s :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c42 :: c6:c7 -> c53:c54:c55:c56 -> c40:c41:c42:c43 a__isNatKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 A__ISNATKIND :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c53:c54:c55:c56 c43 :: c40:c41:c42:c43 c44 :: c10:c11 -> c48:c49:c50:c51:c52 -> c44:c45:c46:c47 zeros :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c45 :: c44:c45:c46:c47 cons :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c46 :: c14:c15 -> c38:c39 -> c53:c54:c55:c56 -> c44:c45:c46:c47 a__and :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatIListKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c47 :: c44:c45:c46:c47 nil :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c48 :: c48:c49:c50:c51:c52 c49 :: c48:c49:c50:c51:c52 c50 :: c38:c39 -> c53:c54:c55:c56 -> c48:c49:c50:c51:c52 take :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c51 :: c38:c39 -> c53:c54:c55:c56 -> c48:c49:c50:c51:c52 c52 :: c48:c49:c50:c51:c52 c53 :: c53:c54:c55:c56 c54 :: c48:c49:c50:c51:c52 -> c53:c54:c55:c56 c55 :: c53:c54:c55:c56 -> c53:c54:c55:c56 c56 :: c53:c54:c55:c56 c57 :: c57:c58:c59:c60 c58 :: c20:c21 -> c38:c39 -> c53:c54:c55:c56 -> c57:c58:c59:c60 c59 :: c26:c27 -> c38:c39 -> c53:c54:c55:c56 -> c57:c58:c59:c60 c60 :: c57:c58:c59:c60 c61 :: c61:c62:c63 c62 :: c32:c33 -> c38:c39 -> c38:c39 -> c57:c58:c59:c60 -> c61:c62:c63 and :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNat :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatKind :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c63 :: c61:c62:c63 A__TAKE :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> c64:c65:c66 c64 :: c34:c35 -> c38:c39 -> c44:c45:c46:c47 -> c64:c65:c66 c65 :: c36:c37 -> c38:c39 -> c38:c39 -> c44:c45:c46:c47 -> c64:c65:c66 c66 :: c64:c65:c66 c67 :: c:c1 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U11 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c68 :: c2:c3 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U12 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c69 :: c4:c5 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 isNatList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c70 :: c57:c58:c59:c60 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U21 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c71 :: c6:c7 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U22 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c72 :: c8:c9 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 c73 :: c40:c41:c42:c43 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U31 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c74 :: c10:c11 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U32 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c75 :: c12:c13 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U41 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c76 :: c14:c15 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U42 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c77 :: c16:c17 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U43 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c78 :: c18:c19 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 isNatIList :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c79 :: c44:c45:c46:c47 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U51 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c80 :: c20:c21 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U52 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c81 :: c22:c23 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U53 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c82 :: c24:c25 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U61 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c83 :: c26:c27 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 U62 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 c84 :: c28:c29 -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 -> 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c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 a__zeros :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U11 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U12 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U21 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U22 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U31 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U32 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 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tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U43 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U51 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U52 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U53 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U61 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U62 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U63 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U71 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__length :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U81 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U91 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__take :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 hole_c:c11_100 :: c:c1 hole_c2:c32_100 :: c2:c3 hole_tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U913_100 :: tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 hole_c4:c54_100 :: c4:c5 hole_c57:c58:c59:c605_100 :: c57:c58:c59:c60 hole_c6:c76_100 :: c6:c7 hole_c8:c97_100 :: c8:c9 hole_c40:c41:c42:c438_100 :: c40:c41:c42:c43 hole_c10:c119_100 :: c10:c11 hole_c12:c1310_100 :: c12:c13 hole_c14:c1511_100 :: c14:c15 hole_c16:c1712_100 :: c16:c17 hole_c18:c1913_100 :: c18:c19 hole_c44:c45:c46:c4714_100 :: c44:c45:c46:c47 hole_c20:c2115_100 :: c20:c21 hole_c22:c2316_100 :: c22:c23 hole_c24:c2517_100 :: c24:c25 hole_c26:c2718_100 :: c26:c27 hole_c28:c2919_100 :: c28:c29 hole_c30:c3120_100 :: c30:c31 hole_c32:c3321_100 :: c32:c33 hole_c61:c62:c6322_100 :: c61:c62:c63 hole_c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c9923_100 :: c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 hole_c34:c3524_100 :: c34:c35 hole_c36:c3725_100 :: c36:c37 hole_c38:c3926_100 :: c38:c39 hole_c48:c49:c50:c51:c5227_100 :: c48:c49:c50:c51:c52 hole_c53:c54:c55:c5628_100 :: c53:c54:c55:c56 hole_c64:c65:c6629_100 :: c64:c65:c66 gen_tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U9130_100 :: Nat -> tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 gen_c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c9931_100 :: Nat -> c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c99 gen_c53:c54:c55:c5632_100 :: Nat -> c53:c54:c55:c56 Generator Equations: gen_tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U9130_100(0) <=> tt gen_tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U9130_100(+(x, 1)) <=> length(gen_tt:0':length:s:zeros:cons:isNatIListKind:nil:take:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U9130_100(x)) gen_c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c9931_100(0) <=> c67(c) gen_c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c9931_100(+(x, 1)) <=> c68(c2(c4, c57), gen_c67:c68:c69:c70:c71:c72:c73:c74:c75:c76:c77:c78:c79:c80:c81:c82:c83:c84:c85:c86:c87:c88:c89:c90:c91:c92:c93:c94:c95:c96:c97:c98:c9931_100(x)) gen_c53:c54:c55:c5632_100(0) <=> c53 gen_c53:c54:c55:c5632_100(+(x, 1)) <=> c55(gen_c53:c54:c55:c5632_100(x)) The following defined symbols remain to be analysed: a__U51, A__U11, a__isNatList, A__ISNATLIST, A__U21, a__isNat, A__ISNAT, A__U31, A__U41, A__U42, a__isNatIList, A__ISNATILIST, A__U51, A__U52, A__U61, A__U62, A__U71, A__LENGTH, mark, MARK, A__U91, A__AND, a__isNatIListKind, A__ISNATILISTKIND, a__isNatKind, A__ISNATKIND, a__and, a__U11, a__U21, a__U31, a__U41, a__U42, a__U52, a__U61, a__U62, a__U71, a__length, a__U91 They will be analysed ascendingly in the following order: a__isNatList < A__U11 A__U11 = A__ISNATLIST A__U11 = A__U21 A__U11 = A__ISNAT A__U11 = A__U31 A__U11 = A__U41 A__U11 = A__U42 A__U11 = A__ISNATILIST A__U11 = A__U51 A__U11 = A__U52 A__U11 = A__U61 A__U11 = A__U62 A__U11 = A__U71 A__U11 = A__LENGTH A__U11 = MARK A__U11 = A__U91 A__U11 = A__AND A__U11 = A__ISNATILISTKIND A__U11 = A__ISNATKIND a__isNatList = a__isNat a__isNatList < A__U31 a__isNatList = a__isNatIList a__isNatList < A__U52 a__isNatList < A__LENGTH a__isNatList = mark a__isNatList = a__isNatIListKind a__isNatList = a__isNatKind a__isNatList = a__and a__isNatList = a__U11 a__isNatList = a__U21 a__isNatList = a__U31 a__isNatList = a__U41 a__isNatList = a__U42 a__isNatList = a__U51 a__isNatList = a__U52 a__isNatList = a__U61 a__isNatList = a__U62 a__isNatList = a__U71 a__isNatList = a__length a__isNatList = a__U91 A__ISNATLIST = A__U21 A__ISNATLIST = A__ISNAT A__ISNATLIST = A__U31 A__ISNATLIST = A__U41 A__ISNATLIST = A__U42 A__ISNATLIST = A__ISNATILIST A__ISNATLIST = A__U51 A__ISNATLIST = A__U52 A__ISNATLIST = A__U61 A__ISNATLIST = A__U62 A__ISNATLIST = A__U71 A__ISNATLIST = A__LENGTH A__ISNATLIST = MARK A__ISNATLIST = A__U91 A__ISNATLIST = A__AND A__ISNATLIST = A__ISNATILISTKIND a__isNatKind < A__ISNATLIST A__ISNATLIST = A__ISNATKIND a__and < A__ISNATLIST a__isNat < A__U21 A__U21 = A__ISNAT A__U21 = A__U31 A__U21 = A__U41 A__U21 = A__U42 A__U21 = A__ISNATILIST A__U21 = A__U51 A__U21 = A__U52 A__U21 = A__U61 A__U21 = A__U62 A__U21 = A__U71 A__U21 = A__LENGTH A__U21 = MARK A__U21 = A__U91 A__U21 = A__AND A__U21 = A__ISNATILISTKIND A__U21 = A__ISNATKIND a__isNat < A__U41 a__isNat = a__isNatIList a__isNat < A__U51 a__isNat < A__U61 a__isNat = mark a__isNat = a__isNatIListKind a__isNat = a__isNatKind a__isNat = a__and a__isNat = a__U11 a__isNat = a__U21 a__isNat = a__U31 a__isNat = a__U41 a__isNat = a__U42 a__isNat = a__U51 a__isNat = a__U52 a__isNat = a__U61 a__isNat = a__U62 a__isNat = a__U71 a__isNat = a__length a__isNat = a__U91 A__ISNAT = A__U31 A__ISNAT = A__U41 A__ISNAT = A__U42 A__ISNAT = A__ISNATILIST A__ISNAT = A__U51 A__ISNAT = A__U52 A__ISNAT = A__U61 A__ISNAT = A__U62 A__ISNAT = A__U71 A__ISNAT = A__LENGTH A__ISNAT = MARK A__ISNAT = A__U91 A__ISNAT = A__AND a__isNatIListKind < A__ISNAT A__ISNAT = A__ISNATILISTKIND a__isNatKind < A__ISNAT A__ISNAT = A__ISNATKIND A__U31 = A__U41 A__U31 = A__U42 A__U31 = A__ISNATILIST A__U31 = A__U51 A__U31 = A__U52 A__U31 = A__U61 A__U31 = A__U62 A__U31 = A__U71 A__U31 = A__LENGTH A__U31 = MARK A__U31 = A__U91 A__U31 = A__AND A__U31 = A__ISNATILISTKIND A__U31 = A__ISNATKIND A__U41 = A__U42 A__U41 = A__ISNATILIST A__U41 = A__U51 A__U41 = A__U52 A__U41 = A__U61 A__U41 = A__U62 A__U41 = A__U71 A__U41 = A__LENGTH A__U41 = MARK A__U41 = A__U91 A__U41 = A__AND A__U41 = A__ISNATILISTKIND A__U41 = A__ISNATKIND a__isNatIList < A__U42 A__U42 = A__ISNATILIST A__U42 = A__U51 A__U42 = A__U52 A__U42 = A__U61 A__U42 = A__U62 A__U42 = A__U71 A__U42 = A__LENGTH A__U42 = MARK A__U42 = A__U91 A__U42 = A__AND A__U42 = A__ISNATILISTKIND A__U42 = A__ISNATKIND a__isNatIList < A__U62 a__isNatIList = mark a__isNatIList < MARK a__isNatIList = a__isNatIListKind a__isNatIList = a__isNatKind a__isNatIList = a__and a__isNatIList = a__U11 a__isNatIList = a__U21 a__isNatIList = a__U31 a__isNatIList = a__U41 a__isNatIList = a__U42 a__isNatIList = a__U51 a__isNatIList = a__U52 a__isNatIList = a__U61 a__isNatIList = a__U62 a__isNatIList = a__U71 a__isNatIList = a__length a__isNatIList = a__U91 A__ISNATILIST = A__U51 A__ISNATILIST = A__U52 A__ISNATILIST = A__U61 A__ISNATILIST = A__U62 A__ISNATILIST = A__U71 A__ISNATILIST = A__LENGTH A__ISNATILIST = MARK A__ISNATILIST = A__U91 A__ISNATILIST = A__AND a__isNatIListKind < A__ISNATILIST A__ISNATILIST = A__ISNATILISTKIND a__isNatKind < A__ISNATILIST A__ISNATILIST = A__ISNATKIND a__and < A__ISNATILIST A__U51 = A__U52 A__U51 = A__U61 A__U51 = A__U62 A__U51 = A__U71 A__U51 = A__LENGTH A__U51 = MARK A__U51 = A__U91 A__U51 = A__AND A__U51 = A__ISNATILISTKIND A__U51 = A__ISNATKIND A__U52 = A__U61 A__U52 = A__U62 A__U52 = A__U71 A__U52 = A__LENGTH A__U52 = MARK A__U52 = A__U91 A__U52 = A__AND A__U52 = A__ISNATILISTKIND A__U52 = A__ISNATKIND A__U61 = A__U62 A__U61 = A__U71 A__U61 = A__LENGTH A__U61 = MARK A__U61 = A__U91 A__U61 = A__AND A__U61 = A__ISNATILISTKIND A__U61 = A__ISNATKIND A__U62 = A__U71 A__U62 = A__LENGTH A__U62 = MARK A__U62 = A__U91 A__U62 = A__AND A__U62 = A__ISNATILISTKIND A__U62 = A__ISNATKIND A__U71 = A__LENGTH mark < A__U71 A__U71 = MARK A__U71 = A__U91 A__U71 = A__AND A__U71 = A__ISNATILISTKIND A__U71 = A__ISNATKIND A__LENGTH = MARK A__LENGTH = A__U91 A__LENGTH = A__AND A__LENGTH = A__ISNATILISTKIND A__LENGTH = A__ISNATKIND a__and < A__LENGTH mark < MARK mark = a__isNatIListKind mark = a__isNatKind mark = a__and mark = a__U11 mark = a__U21 mark = a__U31 mark = a__U41 mark = a__U42 mark = a__U51 mark = a__U52 mark = a__U61 mark = a__U62 mark = a__U71 mark = a__length mark = a__U91 MARK = A__U91 MARK = A__AND MARK = A__ISNATILISTKIND MARK = A__ISNATKIND a__and < MARK A__U91 = A__AND A__U91 = A__ISNATILISTKIND A__U91 = A__ISNATKIND A__AND = A__ISNATILISTKIND A__AND = A__ISNATKIND a__isNatIListKind = a__isNatKind a__isNatIListKind = a__and a__isNatIListKind = a__U11 a__isNatIListKind = a__U21 a__isNatIListKind = a__U31 a__isNatIListKind = a__U41 a__isNatIListKind = a__U42 a__isNatIListKind = a__U51 a__isNatIListKind = a__U52 a__isNatIListKind = a__U61 a__isNatIListKind = a__U62 a__isNatIListKind = a__U71 a__isNatIListKind = a__length a__isNatIListKind = a__U91 a__isNatKind < A__ISNATILISTKIND A__ISNATILISTKIND = A__ISNATKIND a__isNatKind = a__and a__isNatKind = a__U11 a__isNatKind = a__U21 a__isNatKind = a__U31 a__isNatKind = a__U41 a__isNatKind = a__U42 a__isNatKind = a__U51 a__isNatKind = a__U52 a__isNatKind = a__U61 a__isNatKind = a__U62 a__isNatKind = a__U71 a__isNatKind = a__length a__isNatKind = a__U91 a__and = a__U11 a__and = a__U21 a__and = a__U31 a__and = a__U41 a__and = a__U42 a__and = a__U51 a__and = a__U52 a__and = a__U61 a__and = a__U62 a__and = a__U71 a__and = a__length a__and = a__U91 a__U11 = a__U21 a__U11 = a__U31 a__U11 = a__U41 a__U11 = a__U42 a__U11 = a__U51 a__U11 = a__U52 a__U11 = a__U61 a__U11 = a__U62 a__U11 = a__U71 a__U11 = a__length a__U11 = a__U91 a__U21 = a__U31 a__U21 = a__U41 a__U21 = a__U42 a__U21 = a__U51 a__U21 = a__U52 a__U21 = a__U61 a__U21 = a__U62 a__U21 = a__U71 a__U21 = a__length a__U21 = a__U91 a__U31 = a__U41 a__U31 = a__U42 a__U31 = a__U51 a__U31 = a__U52 a__U31 = a__U61 a__U31 = a__U62 a__U31 = a__U71 a__U31 = a__length a__U31 = a__U91 a__U41 = a__U42 a__U41 = a__U51 a__U41 = a__U52 a__U41 = a__U61 a__U41 = a__U62 a__U41 = a__U71 a__U41 = a__length a__U41 = a__U91 a__U42 = a__U51 a__U42 = a__U52 a__U42 = a__U61 a__U42 = a__U62 a__U42 = a__U71 a__U42 = a__length a__U42 = a__U91 a__U51 = a__U52 a__U51 = a__U61 a__U51 = a__U62 a__U51 = a__U71 a__U51 = a__length a__U51 = a__U91 a__U52 = a__U61 a__U52 = a__U62 a__U52 = a__U71 a__U52 = a__length a__U52 = a__U91 a__U61 = a__U62 a__U61 = a__U71 a__U61 = a__length a__U61 = a__U91 a__U62 = a__U71 a__U62 = a__length a__U62 = a__U91 a__U71 = a__length a__U71 = a__U91 a__length = a__U91 ---------------------------------------- (17) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (18) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__U11(tt, V1) -> a__U12(a__isNatList(V1)) [1] a__U12(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1] a__U22(tt) -> tt [1] a__U31(tt, V) -> a__U32(a__isNatList(V)) [1] a__U32(tt) -> tt [1] a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2) [1] a__U42(tt, V2) -> a__U43(a__isNatIList(V2)) [1] a__U43(tt) -> tt [1] a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2) [1] a__U52(tt, V2) -> a__U53(a__isNatList(V2)) [1] a__U53(tt) -> tt [1] a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2) [1] a__U62(tt, V2) -> a__U63(a__isNatIList(V2)) [1] a__U63(tt) -> tt [1] a__U71(tt, L) -> s(a__length(mark(L))) [1] a__U81(tt) -> nil [1] a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) [1] a__isNatIList(zeros) -> tt [1] a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1] a__isNatIListKind(nil) -> tt [1] a__isNatIListKind(zeros) -> tt [1] a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1] a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1] a__isNatKind(0) -> tt [1] a__isNatKind(length(V1)) -> a__isNatIListKind(V1) [1] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__isNatList(nil) -> tt [1] a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1] a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [1] a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) [1] a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X)) -> a__U12(mark(X)) [1] mark(isNatList(X)) -> a__isNatList(X) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X)) -> a__U22(mark(X)) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U32(X)) -> a__U32(mark(X)) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(U42(X1, X2)) -> a__U42(mark(X1), X2) [1] mark(U43(X)) -> a__U43(mark(X)) [1] mark(isNatIList(X)) -> a__isNatIList(X) [1] mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) [1] mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1] mark(U53(X)) -> a__U53(mark(X)) [1] mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1] mark(U62(X1, X2)) -> a__U62(mark(X1), X2) [1] mark(U63(X)) -> a__U63(mark(X)) [1] mark(U71(X1, X2)) -> a__U71(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U81(X)) -> a__U81(mark(X)) [1] mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(isNatIListKind(X)) -> a__isNatIListKind(X) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNatList(X) -> isNatList(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__isNat(X) -> isNat(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__U42(X1, X2) -> U42(X1, X2) [1] a__U43(X) -> U43(X) [1] a__isNatIList(X) -> isNatIList(X) [1] a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1] a__U52(X1, X2) -> U52(X1, X2) [1] a__U53(X) -> U53(X) [1] a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1] a__U62(X1, X2) -> U62(X1, X2) [1] a__U63(X) -> U63(X) [1] a__U71(X1, X2) -> U71(X1, X2) [1] a__length(X) -> length(X) [1] a__U81(X) -> U81(X) [1] a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatIListKind(X) -> isNatIListKind(X) [1] a__isNatKind(X) -> isNatKind(X) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (19) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (20) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__U11(tt, V1) -> a__U12(a__isNatList(V1)) [1] a__U12(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1] a__U22(tt) -> tt [1] a__U31(tt, V) -> a__U32(a__isNatList(V)) [1] a__U32(tt) -> tt [1] a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2) [1] a__U42(tt, V2) -> a__U43(a__isNatIList(V2)) [1] a__U43(tt) -> tt [1] a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2) [1] a__U52(tt, V2) -> a__U53(a__isNatList(V2)) [1] a__U53(tt) -> tt [1] a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2) [1] a__U62(tt, V2) -> a__U63(a__isNatIList(V2)) [1] a__U63(tt) -> tt [1] a__U71(tt, L) -> s(a__length(mark(L))) [1] a__U81(tt) -> nil [1] a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) [1] a__isNatIList(zeros) -> tt [1] a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1] a__isNatIListKind(nil) -> tt [1] a__isNatIListKind(zeros) -> tt [1] a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1] a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1] a__isNatKind(0) -> tt [1] a__isNatKind(length(V1)) -> a__isNatIListKind(V1) [1] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__isNatList(nil) -> tt [1] a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1] a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [1] a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) [1] a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X)) -> a__U12(mark(X)) [1] mark(isNatList(X)) -> a__isNatList(X) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X)) -> a__U22(mark(X)) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U32(X)) -> a__U32(mark(X)) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(U42(X1, X2)) -> a__U42(mark(X1), X2) [1] mark(U43(X)) -> a__U43(mark(X)) [1] mark(isNatIList(X)) -> a__isNatIList(X) [1] mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) [1] mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1] mark(U53(X)) -> a__U53(mark(X)) [1] mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1] mark(U62(X1, X2)) -> a__U62(mark(X1), X2) [1] mark(U63(X)) -> a__U63(mark(X)) [1] mark(U71(X1, X2)) -> a__U71(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U81(X)) -> a__U81(mark(X)) [1] mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(isNatIListKind(X)) -> a__isNatIListKind(X) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNatList(X) -> isNatList(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__isNat(X) -> isNat(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__U42(X1, X2) -> U42(X1, X2) [1] a__U43(X) -> U43(X) [1] a__isNatIList(X) -> isNatIList(X) [1] a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1] a__U52(X1, X2) -> U52(X1, X2) [1] a__U53(X) -> U53(X) [1] a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1] a__U62(X1, X2) -> U62(X1, X2) [1] a__U63(X) -> U63(X) [1] a__U71(X1, X2) -> U71(X1, X2) [1] a__length(X) -> length(X) [1] a__U81(X) -> U81(X) [1] a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatIListKind(X) -> isNatIListKind(X) [1] a__isNatKind(X) -> isNatKind(X) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 cons :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 0 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 tt :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 s :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 mark :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 nil :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 Rewrite Strategy: INNERMOST ---------------------------------------- (21) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: mark_1 a__isNat_1 a__and_2 a__isNatIList_1 a__isNatList_1 a__isNatIListKind_1 a__isNatKind_1 a__U22_1 a__U53_1 a__U32_1 a__U63_1 a__length_1 a__take_2 a__zeros a__U81_1 a__U71_2 a__U31_2 a__U62_2 a__U61_3 a__U42_2 a__U91_4 a__U21_2 a__U43_1 a__U12_1 a__U51_3 a__U41_3 a__U11_2 a__U52_2 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (22) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__U11(tt, V1) -> a__U12(a__isNatList(V1)) [1] a__U12(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1] a__U22(tt) -> tt [1] a__U31(tt, V) -> a__U32(a__isNatList(V)) [1] a__U32(tt) -> tt [1] a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2) [1] a__U42(tt, V2) -> a__U43(a__isNatIList(V2)) [1] a__U43(tt) -> tt [1] a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2) [1] a__U52(tt, V2) -> a__U53(a__isNatList(V2)) [1] a__U53(tt) -> tt [1] a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2) [1] a__U62(tt, V2) -> a__U63(a__isNatIList(V2)) [1] a__U63(tt) -> tt [1] a__U71(tt, L) -> s(a__length(mark(L))) [1] a__U81(tt) -> nil [1] a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) [1] a__isNatIList(zeros) -> tt [1] a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1] a__isNatIListKind(nil) -> tt [1] a__isNatIListKind(zeros) -> tt [1] a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1] a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1] a__isNatKind(0) -> tt [1] a__isNatKind(length(V1)) -> a__isNatIListKind(V1) [1] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__isNatList(nil) -> tt [1] a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1] a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [1] a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) [1] a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X)) -> a__U12(mark(X)) [1] mark(isNatList(X)) -> a__isNatList(X) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X)) -> a__U22(mark(X)) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U32(X)) -> a__U32(mark(X)) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(U42(X1, X2)) -> a__U42(mark(X1), X2) [1] mark(U43(X)) -> a__U43(mark(X)) [1] mark(isNatIList(X)) -> a__isNatIList(X) [1] mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) [1] mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1] mark(U53(X)) -> a__U53(mark(X)) [1] mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1] mark(U62(X1, X2)) -> a__U62(mark(X1), X2) [1] mark(U63(X)) -> a__U63(mark(X)) [1] mark(U71(X1, X2)) -> a__U71(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U81(X)) -> a__U81(mark(X)) [1] mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(isNatIListKind(X)) -> a__isNatIListKind(X) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNatList(X) -> isNatList(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__isNat(X) -> isNat(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__U42(X1, X2) -> U42(X1, X2) [1] a__U43(X) -> U43(X) [1] a__isNatIList(X) -> isNatIList(X) [1] a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1] a__U52(X1, X2) -> U52(X1, X2) [1] a__U53(X) -> U53(X) [1] a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1] a__U62(X1, X2) -> U62(X1, X2) [1] a__U63(X) -> U63(X) [1] a__U71(X1, X2) -> U71(X1, X2) [1] a__length(X) -> length(X) [1] a__U81(X) -> U81(X) [1] a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatIListKind(X) -> isNatIListKind(X) [1] a__isNatKind(X) -> isNatKind(X) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 cons :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 0 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 tt :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 s :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 mark :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 nil :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 Rewrite Strategy: INNERMOST ---------------------------------------- (23) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (24) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__U11(tt, nil) -> a__U12(tt) [2] a__U11(tt, cons(V1', V2')) -> a__U12(a__U51(a__and(a__isNatKind(V1'), isNatIListKind(V2')), V1', V2')) [2] a__U11(tt, take(V1'', V2'')) -> a__U12(a__U61(a__and(a__isNatKind(V1''), isNatIListKind(V2'')), V1'', V2'')) [2] a__U11(tt, V1) -> a__U12(isNatList(V1)) [2] a__U12(tt) -> tt [1] a__U21(tt, 0) -> a__U22(tt) [2] a__U21(tt, length(V11)) -> a__U22(a__U11(a__isNatIListKind(V11), V11)) [2] a__U21(tt, s(V12)) -> a__U22(a__U21(a__isNatKind(V12), V12)) [2] a__U21(tt, V1) -> a__U22(isNat(V1)) [2] a__U22(tt) -> tt [1] a__U31(tt, nil) -> a__U32(tt) [2] a__U31(tt, cons(V13, V21)) -> a__U32(a__U51(a__and(a__isNatKind(V13), isNatIListKind(V21)), V13, V21)) [2] a__U31(tt, take(V14, V22)) -> a__U32(a__U61(a__and(a__isNatKind(V14), isNatIListKind(V22)), V14, V22)) [2] a__U31(tt, V) -> a__U32(isNatList(V)) [2] a__U32(tt) -> tt [1] a__U41(tt, 0, V2) -> a__U42(tt, V2) [2] a__U41(tt, length(V15), V2) -> a__U42(a__U11(a__isNatIListKind(V15), V15), V2) [2] a__U41(tt, s(V16), V2) -> a__U42(a__U21(a__isNatKind(V16), V16), V2) [2] a__U41(tt, V1, V2) -> a__U42(isNat(V1), V2) [2] a__U42(tt, V2) -> a__U43(a__U31(a__isNatIListKind(V2), V2)) [2] a__U42(tt, zeros) -> a__U43(tt) [2] a__U42(tt, cons(V17, V23)) -> a__U43(a__U41(a__and(a__isNatKind(V17), isNatIListKind(V23)), V17, V23)) [2] a__U42(tt, V2) -> a__U43(isNatIList(V2)) [2] a__U43(tt) -> tt [1] a__U51(tt, 0, V2) -> a__U52(tt, V2) [2] a__U51(tt, length(V18), V2) -> a__U52(a__U11(a__isNatIListKind(V18), V18), V2) [2] a__U51(tt, s(V19), V2) -> a__U52(a__U21(a__isNatKind(V19), V19), V2) [2] a__U51(tt, V1, V2) -> a__U52(isNat(V1), V2) [2] a__U52(tt, nil) -> a__U53(tt) [2] a__U52(tt, cons(V110, V24)) -> a__U53(a__U51(a__and(a__isNatKind(V110), isNatIListKind(V24)), V110, V24)) [2] a__U52(tt, take(V111, V25)) -> a__U53(a__U61(a__and(a__isNatKind(V111), isNatIListKind(V25)), V111, V25)) [2] a__U52(tt, V2) -> a__U53(isNatList(V2)) [2] a__U53(tt) -> tt [1] a__U61(tt, 0, V2) -> a__U62(tt, V2) [2] a__U61(tt, length(V112), V2) -> a__U62(a__U11(a__isNatIListKind(V112), V112), V2) [2] a__U61(tt, s(V113), V2) -> a__U62(a__U21(a__isNatKind(V113), V113), V2) [2] a__U61(tt, V1, V2) -> a__U62(isNat(V1), V2) [2] a__U62(tt, V2) -> a__U63(a__U31(a__isNatIListKind(V2), V2)) [2] a__U62(tt, zeros) -> a__U63(tt) [2] a__U62(tt, cons(V114, V26)) -> a__U63(a__U41(a__and(a__isNatKind(V114), isNatIListKind(V26)), V114, V26)) [2] a__U62(tt, V2) -> a__U63(isNatIList(V2)) [2] a__U63(tt) -> tt [1] a__U71(tt, L) -> s(a__length(mark(L))) [1] a__U81(tt) -> nil [1] a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(length(nil)) -> a__U11(tt, nil) [2] a__isNat(length(zeros)) -> a__U11(tt, zeros) [2] a__isNat(length(cons(V115, V27))) -> a__U11(a__and(a__isNatKind(V115), isNatIListKind(V27)), cons(V115, V27)) [2] a__isNat(length(take(V116, V28))) -> a__U11(a__and(a__isNatKind(V116), isNatIListKind(V28)), take(V116, V28)) [2] a__isNat(length(V1)) -> a__U11(isNatIListKind(V1), V1) [2] a__isNat(s(0)) -> a__U21(tt, 0) [2] a__isNat(s(length(V117))) -> a__U21(a__isNatIListKind(V117), length(V117)) [2] a__isNat(s(s(V118))) -> a__U21(a__isNatKind(V118), s(V118)) [2] a__isNat(s(V1)) -> a__U21(isNatKind(V1), V1) [2] a__isNatIList(nil) -> a__U31(tt, nil) [2] a__isNatIList(zeros) -> a__U31(tt, zeros) [2] a__isNatIList(cons(V119, V29)) -> a__U31(a__and(a__isNatKind(V119), isNatIListKind(V29)), cons(V119, V29)) [2] a__isNatIList(take(V120, V210)) -> a__U31(a__and(a__isNatKind(V120), isNatIListKind(V210)), take(V120, V210)) [2] a__isNatIList(V) -> a__U31(isNatIListKind(V), V) [2] a__isNatIList(zeros) -> tt [1] a__isNatIList(cons(0, V2)) -> a__U41(a__and(tt, isNatIListKind(V2)), 0, V2) [2] a__isNatIList(cons(length(V121), V2)) -> a__U41(a__and(a__isNatIListKind(V121), isNatIListKind(V2)), length(V121), V2) [2] a__isNatIList(cons(s(V122), V2)) -> a__U41(a__and(a__isNatKind(V122), isNatIListKind(V2)), s(V122), V2) [2] a__isNatIList(cons(V1, V2)) -> a__U41(a__and(isNatKind(V1), isNatIListKind(V2)), V1, V2) [2] a__isNatIListKind(nil) -> tt [1] a__isNatIListKind(zeros) -> tt [1] a__isNatIListKind(cons(0, V2)) -> a__and(tt, isNatIListKind(V2)) [2] a__isNatIListKind(cons(length(V123), V2)) -> a__and(a__isNatIListKind(V123), isNatIListKind(V2)) [2] a__isNatIListKind(cons(s(V124), V2)) -> a__and(a__isNatKind(V124), isNatIListKind(V2)) [2] a__isNatIListKind(cons(V1, V2)) -> a__and(isNatKind(V1), isNatIListKind(V2)) [2] a__isNatIListKind(take(0, V2)) -> a__and(tt, isNatIListKind(V2)) [2] a__isNatIListKind(take(length(V125), V2)) -> a__and(a__isNatIListKind(V125), isNatIListKind(V2)) [2] a__isNatIListKind(take(s(V126), V2)) -> a__and(a__isNatKind(V126), isNatIListKind(V2)) [2] a__isNatIListKind(take(V1, V2)) -> a__and(isNatKind(V1), isNatIListKind(V2)) [2] a__isNatKind(0) -> tt [1] a__isNatKind(length(V1)) -> a__isNatIListKind(V1) [1] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__isNatList(nil) -> tt [1] a__isNatList(cons(0, V2)) -> a__U51(a__and(tt, isNatIListKind(V2)), 0, V2) [2] a__isNatList(cons(length(V127), V2)) -> a__U51(a__and(a__isNatIListKind(V127), isNatIListKind(V2)), length(V127), V2) [2] a__isNatList(cons(s(V128), V2)) -> a__U51(a__and(a__isNatKind(V128), isNatIListKind(V2)), s(V128), V2) [2] a__isNatList(cons(V1, V2)) -> a__U51(a__and(isNatKind(V1), isNatIListKind(V2)), V1, V2) [2] a__isNatList(take(0, V2)) -> a__U61(a__and(tt, isNatIListKind(V2)), 0, V2) [2] a__isNatList(take(length(V129), V2)) -> a__U61(a__and(a__isNatIListKind(V129), isNatIListKind(V2)), length(V129), V2) [2] a__isNatList(take(s(V130), V2)) -> a__U61(a__and(a__isNatKind(V130), isNatIListKind(V2)), s(V130), V2) [2] a__isNatList(take(V1, V2)) -> a__U61(a__and(isNatKind(V1), isNatIListKind(V2)), V1, V2) [2] a__length(nil) -> 0 [1] a__length(cons(N, nil)) -> a__U71(a__and(a__and(tt, isNatIListKind(nil)), and(isNat(N), isNatKind(N))), nil) [2] a__length(cons(N, cons(V131, V211))) -> a__U71(a__and(a__and(a__U51(a__and(a__isNatKind(V131), isNatIListKind(V211)), V131, V211), isNatIListKind(cons(V131, V211))), and(isNat(N), isNatKind(N))), cons(V131, V211)) [2] a__length(cons(N, take(V132, V212))) -> a__U71(a__and(a__and(a__U61(a__and(a__isNatKind(V132), isNatIListKind(V212)), V132, V212), isNatIListKind(take(V132, V212))), and(isNat(N), isNatKind(N))), take(V132, V212)) [2] a__length(cons(N, L)) -> a__U71(a__and(a__and(isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [2] a__take(0, IL) -> a__U81(a__and(a__U31(a__isNatIListKind(IL), IL), isNatIListKind(IL))) [2] a__take(0, zeros) -> a__U81(a__and(tt, isNatIListKind(zeros))) [2] a__take(0, cons(V133, V213)) -> a__U81(a__and(a__U41(a__and(a__isNatKind(V133), isNatIListKind(V213)), V133, V213), isNatIListKind(cons(V133, V213)))) [2] a__take(0, IL) -> a__U81(a__and(isNatIList(IL), isNatIListKind(IL))) [2] a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__U31(a__isNatIListKind(IL), IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) [2] a__take(s(M), cons(N, zeros)) -> a__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), zeros, M, N) [2] a__take(s(M), cons(N, cons(V134, V214))) -> a__U91(a__and(a__and(a__U41(a__and(a__isNatKind(V134), isNatIListKind(V214)), V134, V214), isNatIListKind(cons(V134, V214))), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), cons(V134, V214), M, N) [2] a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) [2] mark(zeros) -> a__zeros [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X)) -> a__U12(mark(X)) [1] mark(isNatList(X)) -> a__isNatList(X) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X)) -> a__U22(mark(X)) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U32(X)) -> a__U32(mark(X)) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(U42(X1, X2)) -> a__U42(mark(X1), X2) [1] mark(U43(X)) -> a__U43(mark(X)) [1] mark(isNatIList(X)) -> a__isNatIList(X) [1] mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) [1] mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1] mark(U53(X)) -> a__U53(mark(X)) [1] mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1] mark(U62(X1, X2)) -> a__U62(mark(X1), X2) [1] mark(U63(X)) -> a__U63(mark(X)) [1] mark(U71(X1, X2)) -> a__U71(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U81(X)) -> a__U81(mark(X)) [1] mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(isNatIListKind(X)) -> a__isNatIListKind(X) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNatList(X) -> isNatList(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__isNat(X) -> isNat(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__U42(X1, X2) -> U42(X1, X2) [1] a__U43(X) -> U43(X) [1] a__isNatIList(X) -> isNatIList(X) [1] a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1] a__U52(X1, X2) -> U52(X1, X2) [1] a__U53(X) -> U53(X) [1] a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1] a__U62(X1, X2) -> U62(X1, X2) [1] a__U63(X) -> U63(X) [1] a__U71(X1, X2) -> U71(X1, X2) [1] a__length(X) -> length(X) [1] a__U81(X) -> U81(X) [1] a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatIListKind(X) -> isNatIListKind(X) [1] a__isNatKind(X) -> isNatKind(X) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 cons :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 0 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 tt :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 s :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 mark :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 nil :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 Rewrite Strategy: INNERMOST ---------------------------------------- (25) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 zeros => 3 tt => 2 nil => 1 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 2 }-> a__U12(a__U61(a__and(a__isNatKind(V1''), 1 + V2''), V1'', V2'')) :|: z = 2, V1'' >= 0, V2'' >= 0, z' = 1 + V1'' + V2'' a__U11(z, z') -{ 2 }-> a__U12(a__U51(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2')) :|: z = 2, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0 a__U11(z, z') -{ 2 }-> a__U12(2) :|: z = 2, z' = 1 a__U11(z, z') -{ 2 }-> a__U12(1 + V1) :|: z = 2, V1 >= 0, z' = V1 a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z) -{ 1 }-> 2 :|: z = 2 a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(V12), V12)) :|: z = 2, V12 >= 0, z' = 1 + V12 a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__isNatIListKind(V11), V11)) :|: z = 2, V11 >= 0, z' = 1 + V11 a__U21(z, z') -{ 2 }-> a__U22(2) :|: z = 2, z' = 0 a__U21(z, z') -{ 2 }-> a__U22(1 + V1) :|: z = 2, V1 >= 0, z' = V1 a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U22(z) -{ 1 }-> 2 :|: z = 2 a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 2 }-> a__U32(a__U61(a__and(a__isNatKind(V14), 1 + V22), V14, V22)) :|: z = 2, V14 >= 0, z' = 1 + V14 + V22, V22 >= 0 a__U31(z, z') -{ 2 }-> a__U32(a__U51(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: z = 2, V21 >= 0, V13 >= 0, z' = 1 + V13 + V21 a__U31(z, z') -{ 2 }-> a__U32(2) :|: z = 2, z' = 1 a__U31(z, z') -{ 2 }-> a__U32(1 + V) :|: z = 2, z' = V, V >= 0 a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U32(z) -{ 1 }-> 2 :|: z = 2 a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U41(z, z', z'') -{ 2 }-> a__U42(a__U21(a__isNatKind(V16), V16), V2) :|: z = 2, z' = 1 + V16, V16 >= 0, V2 >= 0, z'' = V2 a__U41(z, z', z'') -{ 2 }-> a__U42(a__U11(a__isNatIListKind(V15), V15), V2) :|: z = 2, z' = 1 + V15, V2 >= 0, V15 >= 0, z'' = V2 a__U41(z, z', z'') -{ 2 }-> a__U42(2, V2) :|: z = 2, V2 >= 0, z'' = V2, z' = 0 a__U41(z, z', z'') -{ 2 }-> a__U42(1 + V1, V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1 a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U42(z, z') -{ 2 }-> a__U43(a__U41(a__and(a__isNatKind(V17), 1 + V23), V17, V23)) :|: z = 2, z' = 1 + V17 + V23, V23 >= 0, V17 >= 0 a__U42(z, z') -{ 2 }-> a__U43(a__U31(a__isNatIListKind(V2), V2)) :|: z = 2, z' = V2, V2 >= 0 a__U42(z, z') -{ 2 }-> a__U43(2) :|: z = 2, z' = 3 a__U42(z, z') -{ 2 }-> a__U43(1 + V2) :|: z = 2, z' = V2, V2 >= 0 a__U42(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U43(z) -{ 1 }-> 2 :|: z = 2 a__U43(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U51(z, z', z'') -{ 2 }-> a__U52(a__U21(a__isNatKind(V19), V19), V2) :|: z = 2, z' = 1 + V19, V19 >= 0, V2 >= 0, z'' = V2 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U11(a__isNatIListKind(V18), V18), V2) :|: z = 2, V18 >= 0, z' = 1 + V18, V2 >= 0, z'' = V2 a__U51(z, z', z'') -{ 2 }-> a__U52(2, V2) :|: z = 2, V2 >= 0, z'' = V2, z' = 0 a__U51(z, z', z'') -{ 2 }-> a__U52(1 + V1, V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1 a__U51(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U52(z, z') -{ 2 }-> a__U53(a__U61(a__and(a__isNatKind(V111), 1 + V25), V111, V25)) :|: z = 2, V25 >= 0, z' = 1 + V111 + V25, V111 >= 0 a__U52(z, z') -{ 2 }-> a__U53(a__U51(a__and(a__isNatKind(V110), 1 + V24), V110, V24)) :|: z = 2, V110 >= 0, V24 >= 0, z' = 1 + V110 + V24 a__U52(z, z') -{ 2 }-> a__U53(2) :|: z = 2, z' = 1 a__U52(z, z') -{ 2 }-> a__U53(1 + V2) :|: z = 2, z' = V2, V2 >= 0 a__U52(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U53(z) -{ 1 }-> 2 :|: z = 2 a__U53(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U61(z, z', z'') -{ 2 }-> a__U62(a__U21(a__isNatKind(V113), V113), V2) :|: z = 2, V2 >= 0, z' = 1 + V113, z'' = V2, V113 >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(a__U11(a__isNatIListKind(V112), V112), V2) :|: z = 2, V2 >= 0, V112 >= 0, z' = 1 + V112, z'' = V2 a__U61(z, z', z'') -{ 2 }-> a__U62(2, V2) :|: z = 2, V2 >= 0, z'' = V2, z' = 0 a__U61(z, z', z'') -{ 2 }-> a__U62(1 + V1, V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1 a__U61(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U62(z, z') -{ 2 }-> a__U63(a__U41(a__and(a__isNatKind(V114), 1 + V26), V114, V26)) :|: z = 2, z' = 1 + V114 + V26, V114 >= 0, V26 >= 0 a__U62(z, z') -{ 2 }-> a__U63(a__U31(a__isNatIListKind(V2), V2)) :|: z = 2, z' = V2, V2 >= 0 a__U62(z, z') -{ 2 }-> a__U63(2) :|: z = 2, z' = 3 a__U62(z, z') -{ 2 }-> a__U63(1 + V2) :|: z = 2, z' = V2, V2 >= 0 a__U62(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U63(z) -{ 1 }-> 2 :|: z = 2 a__U63(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U71(z, z') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L a__U71(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U81(z) -{ 1 }-> 1 :|: z = 2 a__U81(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U91(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U91(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__and(z, z') -{ 1 }-> mark(X) :|: z = 2, z' = X, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__isNat(z) -{ 2 }-> a__U21(a__isNatKind(V118), 1 + V118) :|: V118 >= 0, z = 1 + (1 + V118) a__isNat(z) -{ 2 }-> a__U21(a__isNatIListKind(V117), 1 + V117) :|: V117 >= 0, z = 1 + (1 + V117) a__isNat(z) -{ 2 }-> a__U21(2, 0) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + V1, V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V115), 1 + V27), 1 + V115 + V27) :|: z = 1 + (1 + V115 + V27), V115 >= 0, V27 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V116), 1 + V28), 1 + V116 + V28) :|: V28 >= 0, z = 1 + (1 + V116 + V28), V116 >= 0 a__isNat(z) -{ 2 }-> a__U11(2, 3) :|: z = 1 + 3 a__isNat(z) -{ 2 }-> a__U11(2, 1) :|: z = 1 + 1 a__isNat(z) -{ 2 }-> a__U11(1 + V1, V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 1 }-> 2 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatKind(V122), 1 + V2), 1 + V122, V2) :|: z = 1 + (1 + V122) + V2, V2 >= 0, V122 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatIListKind(V121), 1 + V2), 1 + V121, V2) :|: V121 >= 0, z = 1 + (1 + V121) + V2, V2 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__and(2, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatIList(z) -{ 2 }-> a__U41(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatIList(z) -{ 2 }-> a__U31(a__and(a__isNatKind(V119), 1 + V29), 1 + V119 + V29) :|: V29 >= 0, z = 1 + V119 + V29, V119 >= 0 a__isNatIList(z) -{ 2 }-> a__U31(a__and(a__isNatKind(V120), 1 + V210), 1 + V120 + V210) :|: V120 >= 0, z = 1 + V120 + V210, V210 >= 0 a__isNatIList(z) -{ 2 }-> a__U31(2, 3) :|: z = 3 a__isNatIList(z) -{ 2 }-> a__U31(2, 1) :|: z = 1 a__isNatIList(z) -{ 2 }-> a__U31(1 + V, V) :|: z = V, V >= 0 a__isNatIList(z) -{ 1 }-> 2 :|: z = 3 a__isNatIList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatKind(V124), 1 + V2) :|: V124 >= 0, V2 >= 0, z = 1 + (1 + V124) + V2 a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatKind(V126), 1 + V2) :|: V2 >= 0, V126 >= 0, z = 1 + (1 + V126) + V2 a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V123), 1 + V2) :|: V2 >= 0, z = 1 + (1 + V123) + V2, V123 >= 0 a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V125), 1 + V2) :|: V125 >= 0, z = 1 + (1 + V125) + V2, V2 >= 0 a__isNatIListKind(z) -{ 2 }-> a__and(2, 1 + V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatIListKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 1 a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 3 a__isNatIListKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatKind(z) -{ 1 }-> a__isNatKind(V1) :|: z = 1 + V1, V1 >= 0 a__isNatKind(z) -{ 1 }-> a__isNatIListKind(V1) :|: z = 1 + V1, V1 >= 0 a__isNatKind(z) -{ 1 }-> 2 :|: z = 0 a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatList(z) -{ 2 }-> a__U61(a__and(a__isNatKind(V130), 1 + V2), 1 + V130, V2) :|: z = 1 + (1 + V130) + V2, V130 >= 0, V2 >= 0 a__isNatList(z) -{ 2 }-> a__U61(a__and(a__isNatIListKind(V129), 1 + V2), 1 + V129, V2) :|: z = 1 + (1 + V129) + V2, V2 >= 0, V129 >= 0 a__isNatList(z) -{ 2 }-> a__U61(a__and(2, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatList(z) -{ 2 }-> a__U61(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatKind(V128), 1 + V2), 1 + V128, V2) :|: V128 >= 0, V2 >= 0, z = 1 + (1 + V128) + V2 a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatIListKind(V127), 1 + V2), 1 + V127, V2) :|: V127 >= 0, V2 >= 0, z = 1 + (1 + V127) + V2 a__isNatList(z) -{ 2 }-> a__U51(a__and(2, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatList(z) -{ 2 }-> a__U51(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 1 }-> 2 :|: z = 1 a__isNatList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__length(z) -{ 2 }-> a__U71(a__and(a__and(a__U61(a__and(a__isNatKind(V132), 1 + V212), V132, V212), 1 + (1 + V132 + V212)), 1 + (1 + N) + (1 + N)), 1 + V132 + V212) :|: z = 1 + N + (1 + V132 + V212), V132 >= 0, N >= 0, V212 >= 0 a__length(z) -{ 2 }-> a__U71(a__and(a__and(a__U51(a__and(a__isNatKind(V131), 1 + V211), V131, V211), 1 + (1 + V131 + V211)), 1 + (1 + N) + (1 + N)), 1 + V131 + V211) :|: V131 >= 0, z = 1 + N + (1 + V131 + V211), V211 >= 0, N >= 0 a__length(z) -{ 2 }-> a__U71(a__and(a__and(2, 1 + 1), 1 + (1 + N) + (1 + N)), 1) :|: z = 1 + N + 1, N >= 0 a__length(z) -{ 2 }-> a__U71(a__and(a__and(1 + L, 1 + L), 1 + (1 + N) + (1 + N)), L) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(a__U41(a__and(a__isNatKind(V134), 1 + V214), V134, V214), 1 + (1 + V134 + V214)), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), 1 + V134 + V214, M, N) :|: z = 1 + M, V214 >= 0, z' = 1 + N + (1 + V134 + V214), M >= 0, V134 >= 0, N >= 0 a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(a__U31(a__isNatIListKind(IL), IL), 1 + IL), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(2, 1 + 3), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), 3, M, N) :|: z = 1 + M, M >= 0, z' = 1 + N + 3, N >= 0 a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(1 + IL, 1 + IL), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 2 }-> a__U81(a__and(a__U41(a__and(a__isNatKind(V133), 1 + V213), V133, V213), 1 + (1 + V133 + V213))) :|: V213 >= 0, z' = 1 + V133 + V213, z = 0, V133 >= 0 a__take(z, z') -{ 2 }-> a__U81(a__and(a__U31(a__isNatIListKind(IL), IL), 1 + IL)) :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 2 }-> a__U81(a__and(2, 1 + 3)) :|: z' = 3, z = 0 a__take(z, z') -{ 2 }-> a__U81(a__and(1 + IL, 1 + IL)) :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__zeros :|: z = 3 mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__length(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatList(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatIListKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatIList(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__and(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U91(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U81(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U71(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U63(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U62(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U61(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U53(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U52(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U51(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U43(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U42(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U41(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U32(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U22(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U21(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U12(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U11(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (27) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: a__U12(z) -{ 1 }-> 2 :|: z = 2 a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U22(z) -{ 1 }-> 2 :|: z = 2 a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U32(z) -{ 1 }-> 2 :|: z = 2 a__U43(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U43(z) -{ 1 }-> 2 :|: z = 2 a__U53(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U53(z) -{ 1 }-> 2 :|: z = 2 a__U63(z) -{ 1 }-> 2 :|: z = 2 a__U63(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U81(z) -{ 1 }-> 1 :|: z = 2 a__U81(z) -{ 1 }-> 1 + X :|: X >= 0, z = X ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 2 }-> a__U12(a__U61(a__and(a__isNatKind(V1''), 1 + V2''), V1'', V2'')) :|: z = 2, V1'' >= 0, V2'' >= 0, z' = 1 + V1'' + V2'' a__U11(z, z') -{ 2 }-> a__U12(a__U51(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2')) :|: z = 2, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0 a__U11(z, z') -{ 3 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U11(z, z') -{ 3 }-> 2 :|: z = 2, V1 >= 0, z' = V1, 1 + V1 = 2 a__U11(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 1, X >= 0, 2 = X a__U11(z, z') -{ 3 }-> 1 + X :|: z = 2, V1 >= 0, z' = V1, X >= 0, 1 + V1 = X a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z) -{ 1 }-> 2 :|: z = 2 a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(V12), V12)) :|: z = 2, V12 >= 0, z' = 1 + V12 a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__isNatIListKind(V11), V11)) :|: z = 2, V11 >= 0, z' = 1 + V11 a__U21(z, z') -{ 3 }-> 2 :|: z = 2, z' = 0, 2 = 2 a__U21(z, z') -{ 3 }-> 2 :|: z = 2, V1 >= 0, z' = V1, 1 + V1 = 2 a__U21(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 0, X >= 0, 2 = X a__U21(z, z') -{ 3 }-> 1 + X :|: z = 2, V1 >= 0, z' = V1, X >= 0, 1 + V1 = X a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U22(z) -{ 1 }-> 2 :|: z = 2 a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 2 }-> a__U32(a__U61(a__and(a__isNatKind(V14), 1 + V22), V14, V22)) :|: z = 2, V14 >= 0, z' = 1 + V14 + V22, V22 >= 0 a__U31(z, z') -{ 2 }-> a__U32(a__U51(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: z = 2, V21 >= 0, V13 >= 0, z' = 1 + V13 + V21 a__U31(z, z') -{ 3 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U31(z, z') -{ 3 }-> 2 :|: z = 2, z' = V, V >= 0, 1 + V = 2 a__U31(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 1, X >= 0, 2 = X a__U31(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = V, V >= 0, X >= 0, 1 + V = X a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U32(z) -{ 1 }-> 2 :|: z = 2 a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U41(z, z', z'') -{ 2 }-> a__U42(a__U21(a__isNatKind(V16), V16), V2) :|: z = 2, z' = 1 + V16, V16 >= 0, V2 >= 0, z'' = V2 a__U41(z, z', z'') -{ 2 }-> a__U42(a__U11(a__isNatIListKind(V15), V15), V2) :|: z = 2, z' = 1 + V15, V2 >= 0, V15 >= 0, z'' = V2 a__U41(z, z', z'') -{ 2 }-> a__U42(2, V2) :|: z = 2, V2 >= 0, z'' = V2, z' = 0 a__U41(z, z', z'') -{ 2 }-> a__U42(1 + V1, V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1 a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U42(z, z') -{ 2 }-> a__U43(a__U41(a__and(a__isNatKind(V17), 1 + V23), V17, V23)) :|: z = 2, z' = 1 + V17 + V23, V23 >= 0, V17 >= 0 a__U42(z, z') -{ 2 }-> a__U43(a__U31(a__isNatIListKind(V2), V2)) :|: z = 2, z' = V2, V2 >= 0 a__U42(z, z') -{ 3 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U42(z, z') -{ 3 }-> 2 :|: z = 2, z' = V2, V2 >= 0, 1 + V2 = 2 a__U42(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 3, X >= 0, 2 = X a__U42(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = V2, V2 >= 0, X >= 0, 1 + V2 = X a__U42(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U43(z) -{ 1 }-> 2 :|: z = 2 a__U43(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U51(z, z', z'') -{ 2 }-> a__U52(a__U21(a__isNatKind(V19), V19), V2) :|: z = 2, z' = 1 + V19, V19 >= 0, V2 >= 0, z'' = V2 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U11(a__isNatIListKind(V18), V18), V2) :|: z = 2, V18 >= 0, z' = 1 + V18, V2 >= 0, z'' = V2 a__U51(z, z', z'') -{ 2 }-> a__U52(2, V2) :|: z = 2, V2 >= 0, z'' = V2, z' = 0 a__U51(z, z', z'') -{ 2 }-> a__U52(1 + V1, V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1 a__U51(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U52(z, z') -{ 2 }-> a__U53(a__U61(a__and(a__isNatKind(V111), 1 + V25), V111, V25)) :|: z = 2, V25 >= 0, z' = 1 + V111 + V25, V111 >= 0 a__U52(z, z') -{ 2 }-> a__U53(a__U51(a__and(a__isNatKind(V110), 1 + V24), V110, V24)) :|: z = 2, V110 >= 0, V24 >= 0, z' = 1 + V110 + V24 a__U52(z, z') -{ 3 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U52(z, z') -{ 3 }-> 2 :|: z = 2, z' = V2, V2 >= 0, 1 + V2 = 2 a__U52(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 1, X >= 0, 2 = X a__U52(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = V2, V2 >= 0, X >= 0, 1 + V2 = X a__U52(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U53(z) -{ 1 }-> 2 :|: z = 2 a__U53(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U61(z, z', z'') -{ 2 }-> a__U62(a__U21(a__isNatKind(V113), V113), V2) :|: z = 2, V2 >= 0, z' = 1 + V113, z'' = V2, V113 >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(a__U11(a__isNatIListKind(V112), V112), V2) :|: z = 2, V2 >= 0, V112 >= 0, z' = 1 + V112, z'' = V2 a__U61(z, z', z'') -{ 2 }-> a__U62(2, V2) :|: z = 2, V2 >= 0, z'' = V2, z' = 0 a__U61(z, z', z'') -{ 2 }-> a__U62(1 + V1, V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1 a__U61(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U62(z, z') -{ 2 }-> a__U63(a__U41(a__and(a__isNatKind(V114), 1 + V26), V114, V26)) :|: z = 2, z' = 1 + V114 + V26, V114 >= 0, V26 >= 0 a__U62(z, z') -{ 2 }-> a__U63(a__U31(a__isNatIListKind(V2), V2)) :|: z = 2, z' = V2, V2 >= 0 a__U62(z, z') -{ 3 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U62(z, z') -{ 3 }-> 2 :|: z = 2, z' = V2, V2 >= 0, 1 + V2 = 2 a__U62(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 3, X >= 0, 2 = X a__U62(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = V2, V2 >= 0, X >= 0, 1 + V2 = X a__U62(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U63(z) -{ 1 }-> 2 :|: z = 2 a__U63(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U71(z, z') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L a__U71(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U81(z) -{ 1 }-> 1 :|: z = 2 a__U81(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U91(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U91(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__and(z, z') -{ 1 }-> mark(X) :|: z = 2, z' = X, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__isNat(z) -{ 2 }-> a__U21(a__isNatKind(V118), 1 + V118) :|: V118 >= 0, z = 1 + (1 + V118) a__isNat(z) -{ 2 }-> a__U21(a__isNatIListKind(V117), 1 + V117) :|: V117 >= 0, z = 1 + (1 + V117) a__isNat(z) -{ 2 }-> a__U21(2, 0) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + V1, V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V115), 1 + V27), 1 + V115 + V27) :|: z = 1 + (1 + V115 + V27), V115 >= 0, V27 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V116), 1 + V28), 1 + V116 + V28) :|: V28 >= 0, z = 1 + (1 + V116 + V28), V116 >= 0 a__isNat(z) -{ 2 }-> a__U11(2, 3) :|: z = 1 + 3 a__isNat(z) -{ 2 }-> a__U11(2, 1) :|: z = 1 + 1 a__isNat(z) -{ 2 }-> a__U11(1 + V1, V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 1 }-> 2 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatKind(V122), 1 + V2), 1 + V122, V2) :|: z = 1 + (1 + V122) + V2, V2 >= 0, V122 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatIListKind(V121), 1 + V2), 1 + V121, V2) :|: V121 >= 0, z = 1 + (1 + V121) + V2, V2 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__and(2, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatIList(z) -{ 2 }-> a__U41(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatIList(z) -{ 2 }-> a__U31(a__and(a__isNatKind(V119), 1 + V29), 1 + V119 + V29) :|: V29 >= 0, z = 1 + V119 + V29, V119 >= 0 a__isNatIList(z) -{ 2 }-> a__U31(a__and(a__isNatKind(V120), 1 + V210), 1 + V120 + V210) :|: V120 >= 0, z = 1 + V120 + V210, V210 >= 0 a__isNatIList(z) -{ 2 }-> a__U31(2, 3) :|: z = 3 a__isNatIList(z) -{ 2 }-> a__U31(2, 1) :|: z = 1 a__isNatIList(z) -{ 2 }-> a__U31(1 + V, V) :|: z = V, V >= 0 a__isNatIList(z) -{ 1 }-> 2 :|: z = 3 a__isNatIList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatKind(V124), 1 + V2) :|: V124 >= 0, V2 >= 0, z = 1 + (1 + V124) + V2 a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatKind(V126), 1 + V2) :|: V2 >= 0, V126 >= 0, z = 1 + (1 + V126) + V2 a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V123), 1 + V2) :|: V2 >= 0, z = 1 + (1 + V123) + V2, V123 >= 0 a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V125), 1 + V2) :|: V125 >= 0, z = 1 + (1 + V125) + V2, V2 >= 0 a__isNatIListKind(z) -{ 2 }-> a__and(2, 1 + V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatIListKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 1 a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 3 a__isNatIListKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatKind(z) -{ 1 }-> a__isNatKind(V1) :|: z = 1 + V1, V1 >= 0 a__isNatKind(z) -{ 1 }-> a__isNatIListKind(V1) :|: z = 1 + V1, V1 >= 0 a__isNatKind(z) -{ 1 }-> 2 :|: z = 0 a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatList(z) -{ 2 }-> a__U61(a__and(a__isNatKind(V130), 1 + V2), 1 + V130, V2) :|: z = 1 + (1 + V130) + V2, V130 >= 0, V2 >= 0 a__isNatList(z) -{ 2 }-> a__U61(a__and(a__isNatIListKind(V129), 1 + V2), 1 + V129, V2) :|: z = 1 + (1 + V129) + V2, V2 >= 0, V129 >= 0 a__isNatList(z) -{ 2 }-> a__U61(a__and(2, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatList(z) -{ 2 }-> a__U61(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatKind(V128), 1 + V2), 1 + V128, V2) :|: V128 >= 0, V2 >= 0, z = 1 + (1 + V128) + V2 a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatIListKind(V127), 1 + V2), 1 + V127, V2) :|: V127 >= 0, V2 >= 0, z = 1 + (1 + V127) + V2 a__isNatList(z) -{ 2 }-> a__U51(a__and(2, 1 + V2), 0, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNatList(z) -{ 2 }-> a__U51(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 1 }-> 2 :|: z = 1 a__isNatList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__length(z) -{ 2 }-> a__U71(a__and(a__and(a__U61(a__and(a__isNatKind(V132), 1 + V212), V132, V212), 1 + (1 + V132 + V212)), 1 + (1 + N) + (1 + N)), 1 + V132 + V212) :|: z = 1 + N + (1 + V132 + V212), V132 >= 0, N >= 0, V212 >= 0 a__length(z) -{ 2 }-> a__U71(a__and(a__and(a__U51(a__and(a__isNatKind(V131), 1 + V211), V131, V211), 1 + (1 + V131 + V211)), 1 + (1 + N) + (1 + N)), 1 + V131 + V211) :|: V131 >= 0, z = 1 + N + (1 + V131 + V211), V211 >= 0, N >= 0 a__length(z) -{ 2 }-> a__U71(a__and(a__and(2, 1 + 1), 1 + (1 + N) + (1 + N)), 1) :|: z = 1 + N + 1, N >= 0 a__length(z) -{ 2 }-> a__U71(a__and(a__and(1 + L, 1 + L), 1 + (1 + N) + (1 + N)), L) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(a__U41(a__and(a__isNatKind(V134), 1 + V214), V134, V214), 1 + (1 + V134 + V214)), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), 1 + V134 + V214, M, N) :|: z = 1 + M, V214 >= 0, z' = 1 + N + (1 + V134 + V214), M >= 0, V134 >= 0, N >= 0 a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(a__U31(a__isNatIListKind(IL), IL), 1 + IL), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(2, 1 + 3), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), 3, M, N) :|: z = 1 + M, M >= 0, z' = 1 + N + 3, N >= 0 a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(1 + IL, 1 + IL), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 2 }-> a__U81(a__and(a__U41(a__and(a__isNatKind(V133), 1 + V213), V133, V213), 1 + (1 + V133 + V213))) :|: V213 >= 0, z' = 1 + V133 + V213, z = 0, V133 >= 0 a__take(z, z') -{ 2 }-> a__U81(a__and(a__U31(a__isNatIListKind(IL), IL), 1 + IL)) :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 2 }-> a__U81(a__and(2, 1 + 3)) :|: z' = 3, z = 0 a__take(z, z') -{ 2 }-> a__U81(a__and(1 + IL, 1 + IL)) :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__length(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatList(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatIListKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatIList(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__and(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U91(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U81(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U71(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U63(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U62(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U61(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U53(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U52(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U51(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U43(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U42(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U41(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U32(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U22(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U21(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U12(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U11(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> 3 :|: z = 3 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> 1 + 0 + 3 :|: z = 3 ---------------------------------------- (29) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 2 }-> a__U12(a__U61(a__and(a__isNatKind(V1''), 1 + V2''), V1'', V2'')) :|: z = 2, V1'' >= 0, V2'' >= 0, z' = 1 + V1'' + V2'' a__U11(z, z') -{ 2 }-> a__U12(a__U51(a__and(a__isNatKind(V1'), 1 + V2'), V1', V2')) :|: z = 2, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0 a__U11(z, z') -{ 3 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U11(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U11(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 1, X >= 0, 2 = X a__U11(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X a__U11(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U12(z) -{ 1 }-> 2 :|: z = 2 a__U12(z) -{ 1 }-> 1 + z :|: z >= 0 a__U21(z, z') -{ 2 }-> a__U22(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z = 2, z' - 1 >= 0 a__U21(z, z') -{ 2 }-> a__U22(a__U11(a__isNatIListKind(z' - 1), z' - 1)) :|: z = 2, z' - 1 >= 0 a__U21(z, z') -{ 3 }-> 2 :|: z = 2, z' = 0, 2 = 2 a__U21(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U21(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 0, X >= 0, 2 = X a__U21(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X a__U21(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U22(z) -{ 1 }-> 2 :|: z = 2 a__U22(z) -{ 1 }-> 1 + z :|: z >= 0 a__U31(z, z') -{ 2 }-> a__U32(a__U61(a__and(a__isNatKind(V14), 1 + V22), V14, V22)) :|: z = 2, V14 >= 0, z' = 1 + V14 + V22, V22 >= 0 a__U31(z, z') -{ 2 }-> a__U32(a__U51(a__and(a__isNatKind(V13), 1 + V21), V13, V21)) :|: z = 2, V21 >= 0, V13 >= 0, z' = 1 + V13 + V21 a__U31(z, z') -{ 3 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U31(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U31(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 1, X >= 0, 2 = X a__U31(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X a__U31(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U32(z) -{ 1 }-> 2 :|: z = 2 a__U32(z) -{ 1 }-> 1 + z :|: z >= 0 a__U41(z, z', z'') -{ 2 }-> a__U42(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z = 2, z' - 1 >= 0, z'' >= 0 a__U41(z, z', z'') -{ 2 }-> a__U42(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0 a__U41(z, z', z'') -{ 2 }-> a__U42(2, z'') :|: z = 2, z'' >= 0, z' = 0 a__U41(z, z', z'') -{ 2 }-> a__U42(1 + z', z'') :|: z = 2, z' >= 0, z'' >= 0 a__U41(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U42(z, z') -{ 2 }-> a__U43(a__U41(a__and(a__isNatKind(V17), 1 + V23), V17, V23)) :|: z = 2, z' = 1 + V17 + V23, V23 >= 0, V17 >= 0 a__U42(z, z') -{ 2 }-> a__U43(a__U31(a__isNatIListKind(z'), z')) :|: z = 2, z' >= 0 a__U42(z, z') -{ 3 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U42(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U42(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 3, X >= 0, 2 = X a__U42(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X a__U42(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U43(z) -{ 1 }-> 2 :|: z = 2 a__U43(z) -{ 1 }-> 1 + z :|: z >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z = 2, z' - 1 >= 0, z'' >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') :|: z = 2, z' - 1 >= 0, z'' >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(2, z'') :|: z = 2, z'' >= 0, z' = 0 a__U51(z, z', z'') -{ 2 }-> a__U52(1 + z', z'') :|: z = 2, z' >= 0, z'' >= 0 a__U51(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U52(z, z') -{ 2 }-> a__U53(a__U61(a__and(a__isNatKind(V111), 1 + V25), V111, V25)) :|: z = 2, V25 >= 0, z' = 1 + V111 + V25, V111 >= 0 a__U52(z, z') -{ 2 }-> a__U53(a__U51(a__and(a__isNatKind(V110), 1 + V24), V110, V24)) :|: z = 2, V110 >= 0, V24 >= 0, z' = 1 + V110 + V24 a__U52(z, z') -{ 3 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U52(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U52(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 1, X >= 0, 2 = X a__U52(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X a__U52(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U53(z) -{ 1 }-> 2 :|: z = 2 a__U53(z) -{ 1 }-> 1 + z :|: z >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0 a__U61(z, z', z'') -{ 2 }-> a__U62(2, z'') :|: z = 2, z'' >= 0, z' = 0 a__U61(z, z', z'') -{ 2 }-> a__U62(1 + z', z'') :|: z = 2, z' >= 0, z'' >= 0 a__U61(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U62(z, z') -{ 2 }-> a__U63(a__U41(a__and(a__isNatKind(V114), 1 + V26), V114, V26)) :|: z = 2, z' = 1 + V114 + V26, V114 >= 0, V26 >= 0 a__U62(z, z') -{ 2 }-> a__U63(a__U31(a__isNatIListKind(z'), z')) :|: z = 2, z' >= 0 a__U62(z, z') -{ 3 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U62(z, z') -{ 3 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U62(z, z') -{ 3 }-> 1 + X :|: z = 2, z' = 3, X >= 0, 2 = X a__U62(z, z') -{ 3 }-> 1 + X :|: z = 2, z' >= 0, X >= 0, 1 + z' = X a__U62(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U63(z) -{ 1 }-> 2 :|: z = 2 a__U63(z) -{ 1 }-> 1 + z :|: z >= 0 a__U71(z, z') -{ 1 }-> 1 + a__length(mark(z')) :|: z = 2, z' >= 0 a__U71(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U81(z) -{ 1 }-> 1 :|: z = 2 a__U81(z) -{ 1 }-> 1 + z :|: z >= 0 a__U91(z, z', z'', z1) -{ 1 }-> 1 + mark(z1) + (1 + z'' + z') :|: z = 2, z'' >= 0, z' >= 0, z1 >= 0 a__U91(z, z', z'', z1) -{ 1 }-> 1 + z + z' + z'' + z1 :|: z >= 0, z'' >= 0, z' >= 0, z1 >= 0 a__and(z, z') -{ 1 }-> mark(z') :|: z = 2, z' >= 0 a__and(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__isNat(z) -{ 2 }-> a__U21(a__isNatKind(z - 2), 1 + (z - 2)) :|: z - 2 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__isNatIListKind(z - 2), 1 + (z - 2)) :|: z - 2 >= 0 a__isNat(z) -{ 2 }-> a__U21(2, 0) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + (z - 1), z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V115), 1 + V27), 1 + V115 + V27) :|: z = 1 + (1 + V115 + V27), V115 >= 0, V27 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__and(a__isNatKind(V116), 1 + V28), 1 + V116 + V28) :|: V28 >= 0, z = 1 + (1 + V116 + V28), V116 >= 0 a__isNat(z) -{ 2 }-> a__U11(2, 3) :|: z = 1 + 3 a__isNat(z) -{ 2 }-> a__U11(2, 1) :|: z = 1 + 1 a__isNat(z) -{ 2 }-> a__U11(1 + (z - 1), z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 1 }-> 2 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + z :|: z >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatKind(V122), 1 + V2), 1 + V122, V2) :|: z = 1 + (1 + V122) + V2, V2 >= 0, V122 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__and(a__isNatIListKind(V121), 1 + V2), 1 + V121, V2) :|: V121 >= 0, z = 1 + (1 + V121) + V2, V2 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__and(2, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0 a__isNatIList(z) -{ 2 }-> a__U41(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatIList(z) -{ 2 }-> a__U31(a__and(a__isNatKind(V119), 1 + V29), 1 + V119 + V29) :|: V29 >= 0, z = 1 + V119 + V29, V119 >= 0 a__isNatIList(z) -{ 2 }-> a__U31(a__and(a__isNatKind(V120), 1 + V210), 1 + V120 + V210) :|: V120 >= 0, z = 1 + V120 + V210, V210 >= 0 a__isNatIList(z) -{ 2 }-> a__U31(2, 3) :|: z = 3 a__isNatIList(z) -{ 2 }-> a__U31(2, 1) :|: z = 1 a__isNatIList(z) -{ 2 }-> a__U31(1 + z, z) :|: z >= 0 a__isNatIList(z) -{ 1 }-> 2 :|: z = 3 a__isNatIList(z) -{ 1 }-> 1 + z :|: z >= 0 a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatKind(V124), 1 + V2) :|: V124 >= 0, V2 >= 0, z = 1 + (1 + V124) + V2 a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatKind(V126), 1 + V2) :|: V2 >= 0, V126 >= 0, z = 1 + (1 + V126) + V2 a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V123), 1 + V2) :|: V2 >= 0, z = 1 + (1 + V123) + V2, V123 >= 0 a__isNatIListKind(z) -{ 2 }-> a__and(a__isNatIListKind(V125), 1 + V2) :|: V125 >= 0, z = 1 + (1 + V125) + V2, V2 >= 0 a__isNatIListKind(z) -{ 2 }-> a__and(2, 1 + (z - 1)) :|: z - 1 >= 0 a__isNatIListKind(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 1 a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 3 a__isNatIListKind(z) -{ 1 }-> 1 + z :|: z >= 0 a__isNatKind(z) -{ 1 }-> a__isNatKind(z - 1) :|: z - 1 >= 0 a__isNatKind(z) -{ 1 }-> a__isNatIListKind(z - 1) :|: z - 1 >= 0 a__isNatKind(z) -{ 1 }-> 2 :|: z = 0 a__isNatKind(z) -{ 1 }-> 1 + z :|: z >= 0 a__isNatList(z) -{ 2 }-> a__U61(a__and(a__isNatKind(V130), 1 + V2), 1 + V130, V2) :|: z = 1 + (1 + V130) + V2, V130 >= 0, V2 >= 0 a__isNatList(z) -{ 2 }-> a__U61(a__and(a__isNatIListKind(V129), 1 + V2), 1 + V129, V2) :|: z = 1 + (1 + V129) + V2, V2 >= 0, V129 >= 0 a__isNatList(z) -{ 2 }-> a__U61(a__and(2, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0 a__isNatList(z) -{ 2 }-> a__U61(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatKind(V128), 1 + V2), 1 + V128, V2) :|: V128 >= 0, V2 >= 0, z = 1 + (1 + V128) + V2 a__isNatList(z) -{ 2 }-> a__U51(a__and(a__isNatIListKind(V127), 1 + V2), 1 + V127, V2) :|: V127 >= 0, V2 >= 0, z = 1 + (1 + V127) + V2 a__isNatList(z) -{ 2 }-> a__U51(a__and(2, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0 a__isNatList(z) -{ 2 }-> a__U51(a__and(1 + V1, 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 1 }-> 2 :|: z = 1 a__isNatList(z) -{ 1 }-> 1 + z :|: z >= 0 a__length(z) -{ 2 }-> a__U71(a__and(a__and(a__U61(a__and(a__isNatKind(V132), 1 + V212), V132, V212), 1 + (1 + V132 + V212)), 1 + (1 + N) + (1 + N)), 1 + V132 + V212) :|: z = 1 + N + (1 + V132 + V212), V132 >= 0, N >= 0, V212 >= 0 a__length(z) -{ 2 }-> a__U71(a__and(a__and(a__U51(a__and(a__isNatKind(V131), 1 + V211), V131, V211), 1 + (1 + V131 + V211)), 1 + (1 + N) + (1 + N)), 1 + V131 + V211) :|: V131 >= 0, z = 1 + N + (1 + V131 + V211), V211 >= 0, N >= 0 a__length(z) -{ 2 }-> a__U71(a__and(a__and(2, 1 + 1), 1 + (1 + (z - 2)) + (1 + (z - 2))), 1) :|: z - 2 >= 0 a__length(z) -{ 2 }-> a__U71(a__and(a__and(1 + L, 1 + L), 1 + (1 + N) + (1 + N)), L) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + z :|: z >= 0 a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(a__U41(a__and(a__isNatKind(V134), 1 + V214), V134, V214), 1 + (1 + V134 + V214)), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + N) + (1 + N))), 1 + V134 + V214, z - 1, N) :|: V214 >= 0, z' = 1 + N + (1 + V134 + V214), z - 1 >= 0, V134 >= 0, N >= 0 a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(a__U31(a__isNatIListKind(IL), IL), 1 + IL), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + N) + (1 + N))), IL, z - 1, N) :|: z - 1 >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(2, 1 + 3), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + (z' - 4)) + (1 + (z' - 4)))), 3, z - 1, z' - 4) :|: z - 1 >= 0, z' - 4 >= 0 a__take(z, z') -{ 2 }-> a__U91(a__and(a__and(1 + IL, 1 + IL), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + N) + (1 + N))), IL, z - 1, N) :|: z - 1 >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 2 }-> a__U81(a__and(a__U41(a__and(a__isNatKind(V133), 1 + V213), V133, V213), 1 + (1 + V133 + V213))) :|: V213 >= 0, z' = 1 + V133 + V213, z = 0, V133 >= 0 a__take(z, z') -{ 2 }-> a__U81(a__and(a__U31(a__isNatIListKind(z'), z'), 1 + z')) :|: z = 0, z' >= 0 a__take(z, z') -{ 2 }-> a__U81(a__and(2, 1 + 3)) :|: z' = 3, z = 0 a__take(z, z') -{ 2 }-> a__U81(a__and(1 + z', 1 + z')) :|: z = 0, z' >= 0 a__take(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__length(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__isNatList(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__isNatKind(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__isNatIListKind(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__isNatIList(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__isNat(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__and(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U91(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U81(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U71(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U63(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U62(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U61(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U53(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U52(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U51(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U43(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U42(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U41(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U32(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U22(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U21(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U12(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> a__U11(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> 3 :|: z = 3 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> 1 + 0 + 3 :|: z = 3 ---------------------------------------- (31) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: none And the following fresh constants: none ---------------------------------------- (32) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__zeros -> cons(0, zeros) [1] a__U11(tt, V1) -> a__U12(a__isNatList(V1)) [1] a__U12(tt) -> tt [1] a__U21(tt, V1) -> a__U22(a__isNat(V1)) [1] a__U22(tt) -> tt [1] a__U31(tt, V) -> a__U32(a__isNatList(V)) [1] a__U32(tt) -> tt [1] a__U41(tt, V1, V2) -> a__U42(a__isNat(V1), V2) [1] a__U42(tt, V2) -> a__U43(a__isNatIList(V2)) [1] a__U43(tt) -> tt [1] a__U51(tt, V1, V2) -> a__U52(a__isNat(V1), V2) [1] a__U52(tt, V2) -> a__U53(a__isNatList(V2)) [1] a__U53(tt) -> tt [1] a__U61(tt, V1, V2) -> a__U62(a__isNat(V1), V2) [1] a__U62(tt, V2) -> a__U63(a__isNatIList(V2)) [1] a__U63(tt) -> tt [1] a__U71(tt, L) -> s(a__length(mark(L))) [1] a__U81(tt) -> nil [1] a__U91(tt, IL, M, N) -> cons(mark(N), take(M, IL)) [1] a__and(tt, X) -> mark(X) [1] a__isNat(0) -> tt [1] a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1), V1) [1] a__isNat(s(V1)) -> a__U21(a__isNatKind(V1), V1) [1] a__isNatIList(V) -> a__U31(a__isNatIListKind(V), V) [1] a__isNatIList(zeros) -> tt [1] a__isNatIList(cons(V1, V2)) -> a__U41(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1] a__isNatIListKind(nil) -> tt [1] a__isNatIListKind(zeros) -> tt [1] a__isNatIListKind(cons(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1] a__isNatIListKind(take(V1, V2)) -> a__and(a__isNatKind(V1), isNatIListKind(V2)) [1] a__isNatKind(0) -> tt [1] a__isNatKind(length(V1)) -> a__isNatIListKind(V1) [1] a__isNatKind(s(V1)) -> a__isNatKind(V1) [1] a__isNatList(nil) -> tt [1] a__isNatList(cons(V1, V2)) -> a__U51(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1] a__isNatList(take(V1, V2)) -> a__U61(a__and(a__isNatKind(V1), isNatIListKind(V2)), V1, V2) [1] a__length(nil) -> 0 [1] a__length(cons(N, L)) -> a__U71(a__and(a__and(a__isNatList(L), isNatIListKind(L)), and(isNat(N), isNatKind(N))), L) [1] a__take(0, IL) -> a__U81(a__and(a__isNatIList(IL), isNatIListKind(IL))) [1] a__take(s(M), cons(N, IL)) -> a__U91(a__and(a__and(a__isNatIList(IL), isNatIListKind(IL)), and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N)))), IL, M, N) [1] mark(zeros) -> a__zeros [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X)) -> a__U12(mark(X)) [1] mark(isNatList(X)) -> a__isNatList(X) [1] mark(U21(X1, X2)) -> a__U21(mark(X1), X2) [1] mark(U22(X)) -> a__U22(mark(X)) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U32(X)) -> a__U32(mark(X)) [1] mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1] mark(U42(X1, X2)) -> a__U42(mark(X1), X2) [1] mark(U43(X)) -> a__U43(mark(X)) [1] mark(isNatIList(X)) -> a__isNatIList(X) [1] mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) [1] mark(U52(X1, X2)) -> a__U52(mark(X1), X2) [1] mark(U53(X)) -> a__U53(mark(X)) [1] mark(U61(X1, X2, X3)) -> a__U61(mark(X1), X2, X3) [1] mark(U62(X1, X2)) -> a__U62(mark(X1), X2) [1] mark(U63(X)) -> a__U63(mark(X)) [1] mark(U71(X1, X2)) -> a__U71(mark(X1), X2) [1] mark(length(X)) -> a__length(mark(X)) [1] mark(U81(X)) -> a__U81(mark(X)) [1] mark(U91(X1, X2, X3, X4)) -> a__U91(mark(X1), X2, X3, X4) [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(isNatIListKind(X)) -> a__isNatIListKind(X) [1] mark(isNatKind(X)) -> a__isNatKind(X) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] a__zeros -> zeros [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNatList(X) -> isNatList(X) [1] a__U21(X1, X2) -> U21(X1, X2) [1] a__U22(X) -> U22(X) [1] a__isNat(X) -> isNat(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1] a__U42(X1, X2) -> U42(X1, X2) [1] a__U43(X) -> U43(X) [1] a__isNatIList(X) -> isNatIList(X) [1] a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1] a__U52(X1, X2) -> U52(X1, X2) [1] a__U53(X) -> U53(X) [1] a__U61(X1, X2, X3) -> U61(X1, X2, X3) [1] a__U62(X1, X2) -> U62(X1, X2) [1] a__U63(X) -> U63(X) [1] a__U71(X1, X2) -> U71(X1, X2) [1] a__length(X) -> length(X) [1] a__U81(X) -> U81(X) [1] a__U91(X1, X2, X3, X4) -> U91(X1, X2, X3, X4) [1] a__take(X1, X2) -> take(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNatIListKind(X) -> isNatIListKind(X) [1] a__isNatKind(X) -> isNatKind(X) [1] The TRS has the following type information: a__zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 cons :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 0 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 zeros :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 tt :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 s :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 mark :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 nil :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 length :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatIListKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 and :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNat :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatKind :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 a__take :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U11 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U12 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U21 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U22 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U31 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U32 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U41 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U42 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U43 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 isNatIList :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U51 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U52 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U53 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U61 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U62 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U63 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U71 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U81 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 U91 :: 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 -> 0:zeros:cons:tt:s:nil:take:length:isNatIListKind:isNat:isNatKind:and:U11:U12:isNatList:U21:U22:U31:U32:U41:U42:U43:isNatIList:U51:U52:U53:U61:U62:U63:U71:U81:U91 Rewrite Strategy: INNERMOST ---------------------------------------- (33) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 zeros => 3 tt => 2 nil => 1 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 1 }-> a__U12(a__isNatList(V1)) :|: z = 2, V1 >= 0, z' = V1 a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z) -{ 1 }-> 2 :|: z = 2 a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z, z') -{ 1 }-> a__U22(a__isNat(V1)) :|: z = 2, V1 >= 0, z' = V1 a__U21(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U22(z) -{ 1 }-> 2 :|: z = 2 a__U22(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 1 }-> a__U32(a__isNatList(V)) :|: z = 2, z' = V, V >= 0 a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U32(z) -{ 1 }-> 2 :|: z = 2 a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U41(z, z', z'') -{ 1 }-> a__U42(a__isNat(V1), V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1 a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U42(z, z') -{ 1 }-> a__U43(a__isNatIList(V2)) :|: z = 2, z' = V2, V2 >= 0 a__U42(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U43(z) -{ 1 }-> 2 :|: z = 2 a__U43(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U51(z, z', z'') -{ 1 }-> a__U52(a__isNat(V1), V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1 a__U51(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U52(z, z') -{ 1 }-> a__U53(a__isNatList(V2)) :|: z = 2, z' = V2, V2 >= 0 a__U52(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U53(z) -{ 1 }-> 2 :|: z = 2 a__U53(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U61(z, z', z'') -{ 1 }-> a__U62(a__isNat(V1), V2) :|: z = 2, V1 >= 0, V2 >= 0, z'' = V2, z' = V1 a__U61(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U62(z, z') -{ 1 }-> a__U63(a__isNatIList(V2)) :|: z = 2, z' = V2, V2 >= 0 a__U62(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U63(z) -{ 1 }-> 2 :|: z = 2 a__U63(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U71(z, z') -{ 1 }-> 1 + a__length(mark(L)) :|: z = 2, L >= 0, z' = L a__U71(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U81(z) -{ 1 }-> 1 :|: z = 2 a__U81(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U91(z, z', z'', z1) -{ 1 }-> 1 + mark(N) + (1 + M + IL) :|: z = 2, z1 = N, z' = IL, M >= 0, IL >= 0, z'' = M, N >= 0 a__U91(z, z', z'', z1) -{ 1 }-> 1 + X1 + X2 + X3 + X4 :|: X1 >= 0, z1 = X4, X3 >= 0, X2 >= 0, X4 >= 0, z = X1, z' = X2, z'' = X3 a__and(z, z') -{ 1 }-> mark(X) :|: z = 2, z' = X, X >= 0 a__and(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__isNat(z) -{ 1 }-> a__U21(a__isNatKind(V1), V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 1 }-> a__U11(a__isNatIListKind(V1), V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 1 }-> 2 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatIList(z) -{ 1 }-> a__U41(a__and(a__isNatKind(V1), 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatIList(z) -{ 1 }-> a__U31(a__isNatIListKind(V), V) :|: z = V, V >= 0 a__isNatIList(z) -{ 1 }-> 2 :|: z = 3 a__isNatIList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatIListKind(z) -{ 1 }-> a__and(a__isNatKind(V1), 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 1 a__isNatIListKind(z) -{ 1 }-> 2 :|: z = 3 a__isNatIListKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatKind(z) -{ 1 }-> a__isNatKind(V1) :|: z = 1 + V1, V1 >= 0 a__isNatKind(z) -{ 1 }-> a__isNatIListKind(V1) :|: z = 1 + V1, V1 >= 0 a__isNatKind(z) -{ 1 }-> 2 :|: z = 0 a__isNatKind(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNatList(z) -{ 1 }-> a__U61(a__and(a__isNatKind(V1), 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 1 }-> a__U51(a__and(a__isNatKind(V1), 1 + V2), V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNatList(z) -{ 1 }-> 2 :|: z = 1 a__isNatList(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__length(z) -{ 1 }-> a__U71(a__and(a__and(a__isNatList(L), 1 + L), 1 + (1 + N) + (1 + N)), L) :|: z = 1 + N + L, L >= 0, N >= 0 a__length(z) -{ 1 }-> 0 :|: z = 1 a__length(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 1 }-> a__U91(a__and(a__and(a__isNatIList(IL), 1 + IL), 1 + (1 + (1 + M) + (1 + M)) + (1 + (1 + N) + (1 + N))), IL, M, N) :|: z = 1 + M, M >= 0, IL >= 0, z' = 1 + N + IL, N >= 0 a__take(z, z') -{ 1 }-> a__U81(a__and(a__isNatIList(IL), 1 + IL)) :|: z' = IL, z = 0, IL >= 0 a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__zeros -{ 1 }-> 3 :|: a__zeros -{ 1 }-> 1 + 0 + 3 :|: mark(z) -{ 1 }-> a__zeros :|: z = 3 mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__length(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatList(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatIListKind(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNatIList(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__and(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U91(mark(X1), X2, X3, X4) :|: X1 >= 0, z = 1 + X1 + X2 + X3 + X4, X3 >= 0, X2 >= 0, X4 >= 0 mark(z) -{ 1 }-> a__U81(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U71(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U63(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U62(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U61(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U53(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U52(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U51(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U43(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U42(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U41(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U32(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U22(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U21(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U12(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U11(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (35) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0)) A__U11(z0, z1) -> c3 A__U12(tt) -> c4 A__U12(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0)) A__U31(z0, z1) -> c11 A__U32(tt) -> c12 A__U32(z0) -> c13 A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U41(z0, z1, z2) -> c15 A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U42(z0, z1) -> c17 A__U43(tt) -> c18 A__U43(z0) -> c19 A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U51(z0, z1, z2) -> c21 A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0)) A__U52(z0, z1) -> c23 A__U53(tt) -> c24 A__U53(z0) -> c25 A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(z0, z1, z2) -> c27 A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U62(z0, z1) -> c29 A__U63(tt) -> c30 A__U63(z0) -> c31 A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U71(z0, z1) -> c33 A__U81(tt) -> c34 A__U81(z0) -> c35 A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__U91(z0, z1, z2, z3) -> c37 A__AND(tt, z0) -> c38(MARK(z0)) A__AND(z0, z1) -> c39 A__ISNAT(0) -> c40 A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c43 A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(zeros) -> c45 A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c47 A__ISNATILISTKIND(nil) -> c48 A__ISNATILISTKIND(zeros) -> c49 A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(z0) -> c52 A__ISNATKIND(0) -> c53 A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c56 A__ISNATLIST(nil) -> c57 A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(z0) -> c60 A__LENGTH(nil) -> c61 A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__LENGTH(z0) -> c63 A__TAKE(0, z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c66 MARK(zeros) -> c67(A__ZEROS) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(0) -> c96 MARK(tt) -> c97 MARK(s(z0)) -> c98(MARK(z0)) MARK(nil) -> c99 S tuples: A__ZEROS -> c A__ZEROS -> c1 A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0)) A__U11(z0, z1) -> c3 A__U12(tt) -> c4 A__U12(z0) -> c5 A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U21(z0, z1) -> c7 A__U22(tt) -> c8 A__U22(z0) -> c9 A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0)) A__U31(z0, z1) -> c11 A__U32(tt) -> c12 A__U32(z0) -> c13 A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U41(z0, z1, z2) -> c15 A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U42(z0, z1) -> c17 A__U43(tt) -> c18 A__U43(z0) -> c19 A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U51(z0, z1, z2) -> c21 A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0)) A__U52(z0, z1) -> c23 A__U53(tt) -> c24 A__U53(z0) -> c25 A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(z0, z1, z2) -> c27 A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U62(z0, z1) -> c29 A__U63(tt) -> c30 A__U63(z0) -> c31 A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U71(z0, z1) -> c33 A__U81(tt) -> c34 A__U81(z0) -> c35 A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__U91(z0, z1, z2, z3) -> c37 A__AND(tt, z0) -> c38(MARK(z0)) A__AND(z0, z1) -> c39 A__ISNAT(0) -> c40 A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNAT(z0) -> c43 A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(zeros) -> c45 A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c47 A__ISNATILISTKIND(nil) -> c48 A__ISNATILISTKIND(zeros) -> c49 A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(z0) -> c52 A__ISNATKIND(0) -> c53 A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATKIND(z0) -> c56 A__ISNATLIST(nil) -> c57 A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(z0) -> c60 A__LENGTH(nil) -> c61 A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__LENGTH(z0) -> c63 A__TAKE(0, z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) A__TAKE(z0, z1) -> c66 MARK(zeros) -> c67(A__ZEROS) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(0) -> c96 MARK(tt) -> c97 MARK(s(z0)) -> c98(MARK(z0)) MARK(nil) -> c99 K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__ZEROS, A__U11_2, A__U12_1, A__U21_2, A__U22_1, A__U31_2, A__U32_1, A__U41_3, A__U42_2, A__U43_1, A__U51_3, A__U52_2, A__U53_1, A__U61_3, A__U62_2, A__U63_1, A__U71_2, A__U81_1, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c, c1, c2_2, c3, c4, c5, c6_2, c7, c8, c9, c10_2, c11, c12, c13, c14_2, c15, c16_2, c17, c18, c19, c20_2, c21, c22_2, c23, c24, c25, c26_2, c27, c28_2, c29, c30, c31, c32_2, c33, c34, c35, c36_1, c37, c38_1, c39, c40, c41_2, c42_2, c43, c44_2, c45, c46_3, c47, c48, c49, c50_2, c51_2, c52, c53, c54_1, c55_1, c56, c57, c58_3, c59_3, c60, c61, c62_4, c63, c64_3, c65_4, c66, c67_1, c68_2, c69_2, c70_1, c71_2, c72_2, c73_1, c74_2, c75_2, c76_2, c77_2, c78_2, c79_1, c80_2, c81_2, c82_2, c83_2, c84_2, c85_2, c86_2, c87_2, c88_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c96, c97, c98_1, c99 ---------------------------------------- (37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 46 trailing nodes: A__ZEROS -> c1 A__U51(z0, z1, z2) -> c21 A__AND(z0, z1) -> c39 A__U62(z0, z1) -> c29 A__U63(tt) -> c30 A__U22(tt) -> c8 A__ISNATILISTKIND(zeros) -> c49 A__ISNATILIST(z0) -> c47 MARK(0) -> c96 A__ISNAT(0) -> c40 A__ISNATLIST(z0) -> c60 A__U42(z0, z1) -> c17 A__U32(z0) -> c13 A__LENGTH(z0) -> c63 MARK(tt) -> c97 A__U43(tt) -> c18 A__U12(z0) -> c5 A__ZEROS -> c A__ISNATLIST(nil) -> c57 A__U53(tt) -> c24 MARK(nil) -> c99 A__U41(z0, z1, z2) -> c15 A__ISNATKIND(0) -> c53 A__U91(z0, z1, z2, z3) -> c37 A__U32(tt) -> c12 A__U81(z0) -> c35 MARK(zeros) -> c67(A__ZEROS) A__U22(z0) -> c9 A__U52(z0, z1) -> c23 A__U63(z0) -> c31 A__U12(tt) -> c4 A__ISNATILISTKIND(nil) -> c48 A__U61(z0, z1, z2) -> c27 A__U21(z0, z1) -> c7 A__ISNAT(z0) -> c43 A__ISNATILISTKIND(z0) -> c52 A__U43(z0) -> c19 A__ISNATKIND(z0) -> c56 A__U81(tt) -> c34 A__ISNATILIST(zeros) -> c45 A__U71(z0, z1) -> c33 A__LENGTH(nil) -> c61 A__TAKE(z0, z1) -> c66 A__U31(z0, z1) -> c11 A__U11(z0, z1) -> c3 A__U53(z0) -> c25 ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0)) A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0)) A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(0, z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) S tuples: A__U11(tt, z0) -> c2(A__U12(a__isNatList(z0)), A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__U22(a__isNat(z0)), A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__U32(a__isNatList(z0)), A__ISNATLIST(z0)) A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U42(tt, z0) -> c16(A__U43(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U52(tt, z0) -> c22(A__U53(a__isNatList(z0)), A__ISNATLIST(z0)) A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U62(tt, z0) -> c28(A__U63(a__isNatIList(z0)), A__ISNATILIST(z0)) A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(0, z0) -> c64(A__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c69(A__U12(mark(z0)), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(U22(z0)) -> c72(A__U22(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c75(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(U43(z0)) -> c78(A__U43(mark(z0)), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U53(z0)) -> c82(A__U53(mark(z0)), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U63(z0)) -> c85(A__U63(mark(z0)), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U81(z0)) -> c88(A__U81(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_2, A__U31_2, A__U41_3, A__U42_2, A__U51_3, A__U52_2, A__U61_3, A__U62_2, A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1 Compound Symbols: c2_2, c6_2, c10_2, c14_2, c16_2, c20_2, c22_2, c26_2, c28_2, c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c64_3, c65_4, c68_2, c69_2, c70_1, c71_2, c72_2, c73_1, c74_2, c75_2, c76_2, c77_2, c78_2, c79_1, c80_2, c81_2, c82_2, c83_2, c84_2, c85_2, c86_2, c87_2, c88_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing tuple parts ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) S tuples: A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2 Compound Symbols: c14_2, c20_2, c26_2, c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1 ---------------------------------------- (41) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (42) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) The (relative) TRS S consists of the following rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Rewrite Strategy: INNERMOST ---------------------------------------- (43) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (44) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (45) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (46) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) [1] A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) [1] A__AND(tt, z0) -> c38(MARK(z0)) [1] A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1] A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1] A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) [1] A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) [1] MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) [1] MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c73(A__ISNAT(z0)) [1] MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) [1] MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) [1] MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) [1] MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) [1] MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) [1] MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) [1] MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) [1] MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) [1] MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) [1] MARK(cons(z0, z1)) -> c95(MARK(z0)) [1] MARK(s(z0)) -> c98(MARK(z0)) [1] A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) [1] A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1] A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) [1] A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) [1] A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) [1] A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) [1] A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) [1] MARK(U12(z0)) -> c69(MARK(z0)) [1] MARK(U22(z0)) -> c72(MARK(z0)) [1] MARK(U32(z0)) -> c75(MARK(z0)) [1] MARK(U43(z0)) -> c78(MARK(z0)) [1] MARK(U53(z0)) -> c82(MARK(z0)) [1] MARK(U63(z0)) -> c85(MARK(z0)) [1] MARK(U81(z0)) -> c88(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt, z0) -> a__U12(a__isNatList(z0)) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U12(tt) -> tt [0] a__U12(z0) -> U12(z0) [0] a__U21(tt, z0) -> a__U22(a__isNat(z0)) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt) -> tt [0] a__U22(z0) -> U22(z0) [0] a__U31(tt, z0) -> a__U32(a__isNatList(z0)) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U32(tt) -> tt [0] a__U32(z0) -> U32(z0) [0] a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) [0] a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0] a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) [0] a__U42(z0, z1) -> U42(z0, z1) [0] a__U43(tt) -> tt [0] a__U43(z0) -> U43(z0) [0] a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) [0] a__U51(z0, z1, z2) -> U51(z0, z1, z2) [0] a__U52(tt, z0) -> a__U53(a__isNatList(z0)) [0] a__U52(z0, z1) -> U52(z0, z1) [0] a__U53(tt) -> tt [0] a__U53(z0) -> U53(z0) [0] a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) [0] a__U61(z0, z1, z2) -> U61(z0, z1, z2) [0] a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) [0] a__U62(z0, z1) -> U62(z0, z1) [0] a__U63(tt) -> tt [0] a__U63(z0) -> U63(z0) [0] a__U71(tt, z0) -> s(a__length(mark(z0))) [0] a__U71(z0, z1) -> U71(z0, z1) [0] a__U81(tt) -> nil [0] a__U81(z0) -> U81(z0) [0] a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__isNat(0) -> tt [0] a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) [0] a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) [0] a__isNatIList(zeros) -> tt [0] a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatIList(z0) -> isNatIList(z0) [0] a__isNatIListKind(nil) -> tt [0] a__isNatIListKind(zeros) -> tt [0] a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) [0] a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) [0] a__isNatIListKind(z0) -> isNatIListKind(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(length(z0)) -> a__isNatIListKind(z0) [0] a__isNatKind(s(z0)) -> a__isNatKind(z0) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__isNatList(nil) -> tt [0] a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatList(z0) -> isNatList(z0) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) [0] a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U12(z0)) -> a__U12(mark(z0)) [0] mark(isNatList(z0)) -> a__isNatList(z0) [0] mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0] mark(U22(z0)) -> a__U22(mark(z0)) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U32(z0)) -> a__U32(mark(z0)) [0] mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0] mark(U42(z0, z1)) -> a__U42(mark(z0), z1) [0] mark(U43(z0)) -> a__U43(mark(z0)) [0] mark(isNatIList(z0)) -> a__isNatIList(z0) [0] mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) [0] mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0] mark(U53(z0)) -> a__U53(mark(z0)) [0] mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) [0] mark(U62(z0, z1)) -> a__U62(mark(z0), z1) [0] mark(U63(z0)) -> a__U63(mark(z0)) [0] mark(U71(z0, z1)) -> a__U71(mark(z0), z1) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(U81(z0)) -> a__U81(mark(z0)) [0] mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] Rewrite Strategy: INNERMOST ---------------------------------------- (47) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (48) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) [1] A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) [1] A__AND(tt, z0) -> c38(MARK(z0)) [1] A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1] A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1] A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) [1] A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) [1] MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) [1] MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c73(A__ISNAT(z0)) [1] MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) [1] MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) [1] MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) [1] MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) [1] MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) [1] MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) [1] MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) [1] MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) [1] MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) [1] MARK(cons(z0, z1)) -> c95(MARK(z0)) [1] MARK(s(z0)) -> c98(MARK(z0)) [1] A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) [1] A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1] A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) [1] A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) [1] A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) [1] A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) [1] A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) [1] MARK(U12(z0)) -> c69(MARK(z0)) [1] MARK(U22(z0)) -> c72(MARK(z0)) [1] MARK(U32(z0)) -> c75(MARK(z0)) [1] MARK(U43(z0)) -> c78(MARK(z0)) [1] MARK(U53(z0)) -> c82(MARK(z0)) [1] MARK(U63(z0)) -> c85(MARK(z0)) [1] MARK(U81(z0)) -> c88(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt, z0) -> a__U12(a__isNatList(z0)) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U12(tt) -> tt [0] a__U12(z0) -> U12(z0) [0] a__U21(tt, z0) -> a__U22(a__isNat(z0)) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt) -> tt [0] a__U22(z0) -> U22(z0) [0] a__U31(tt, z0) -> a__U32(a__isNatList(z0)) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U32(tt) -> tt [0] a__U32(z0) -> U32(z0) [0] a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) [0] a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0] a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) [0] a__U42(z0, z1) -> U42(z0, z1) [0] a__U43(tt) -> tt [0] a__U43(z0) -> U43(z0) [0] a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) [0] a__U51(z0, z1, z2) -> U51(z0, z1, z2) [0] a__U52(tt, z0) -> a__U53(a__isNatList(z0)) [0] a__U52(z0, z1) -> U52(z0, z1) [0] a__U53(tt) -> tt [0] a__U53(z0) -> U53(z0) [0] a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) [0] a__U61(z0, z1, z2) -> U61(z0, z1, z2) [0] a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) [0] a__U62(z0, z1) -> U62(z0, z1) [0] a__U63(tt) -> tt [0] a__U63(z0) -> U63(z0) [0] a__U71(tt, z0) -> s(a__length(mark(z0))) [0] a__U71(z0, z1) -> U71(z0, z1) [0] a__U81(tt) -> nil [0] a__U81(z0) -> U81(z0) [0] a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__isNat(0) -> tt [0] a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) [0] a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) [0] a__isNatIList(zeros) -> tt [0] a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatIList(z0) -> isNatIList(z0) [0] a__isNatIListKind(nil) -> tt [0] a__isNatIListKind(zeros) -> tt [0] a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) [0] a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) [0] a__isNatIListKind(z0) -> isNatIListKind(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(length(z0)) -> a__isNatIListKind(z0) [0] a__isNatKind(s(z0)) -> a__isNatKind(z0) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__isNatList(nil) -> tt [0] a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatList(z0) -> isNatList(z0) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) [0] a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U12(z0)) -> a__U12(mark(z0)) [0] mark(isNatList(z0)) -> a__isNatList(z0) [0] mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0] mark(U22(z0)) -> a__U22(mark(z0)) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U32(z0)) -> a__U32(mark(z0)) [0] mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0] mark(U42(z0, z1)) -> a__U42(mark(z0), z1) [0] mark(U43(z0)) -> a__U43(mark(z0)) [0] mark(isNatIList(z0)) -> a__isNatIList(z0) [0] mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) [0] mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0] mark(U53(z0)) -> a__U53(mark(z0)) [0] mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) [0] mark(U62(z0, z1)) -> a__U62(mark(z0), z1) [0] mark(U63(z0)) -> a__U63(mark(z0)) [0] mark(U71(z0, z1)) -> a__U71(mark(z0), z1) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(U81(z0)) -> a__U81(mark(z0)) [0] mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] The TRS has the following type information: A__U41 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c14 tt :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c14 :: c16 -> c41:c42 -> c14 A__U42 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c16 a__isNat :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil A__ISNAT :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c41:c42 A__U51 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c20 c20 :: c22 -> c41:c42 -> c20 A__U52 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c22 A__U61 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c26 c26 :: c28 -> c41:c42 -> c26 A__U62 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c28 A__U71 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c32 c32 :: c62 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c32 A__LENGTH :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c62 mark :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil MARK :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 A__U91 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c36 c36 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c36 A__AND :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c38 c38 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c38 length :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c41 :: c2 -> c50:c51 -> c41:c42 A__U11 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c2 a__isNatIListKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil A__ISNATILISTKIND :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c50:c51 s :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c42 :: c6 -> c54:c55 -> c41:c42 A__U21 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c6 a__isNatKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil A__ISNATKIND :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c54:c55 A__ISNATILIST :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c44:c46 c44 :: c10 -> c50:c51 -> c44:c46 A__U31 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c10 cons :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c46 :: c14 -> c38 -> c54:c55 -> c44:c46 a__and :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil isNatIListKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c50 :: c38 -> c54:c55 -> c50:c51 take :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c51 :: c38 -> c54:c55 -> c50:c51 c54 :: c50:c51 -> c54:c55 c55 :: c54:c55 -> c54:c55 A__ISNATLIST :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c58:c59 c58 :: c20 -> c38 -> c54:c55 -> c58:c59 c59 :: c26 -> c38 -> c54:c55 -> c58:c59 c62 :: c32 -> c38 -> c38 -> c58:c59 -> c62 a__isNatList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil and :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil isNat :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil isNatKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil A__TAKE :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> c65:c64 c65 :: c36 -> c38 -> c38 -> c44:c46 -> c65:c64 a__isNatIList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil U11 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c68 :: c2 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 isNatList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c70 :: c58:c59 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U21 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c71 :: c6 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c73 :: c41:c42 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U31 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c74 :: c10 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U41 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c76 :: c14 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U42 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c77 :: c16 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 isNatIList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c79 :: c44:c46 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U51 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c80 :: c20 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U52 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c81 :: c22 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U61 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c83 :: c26 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U62 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c84 :: c28 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U71 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c86 :: c32 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c87 :: c62 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U91 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c89 :: c36 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c90 :: c65:c64 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c91 :: c65:c64 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c92 :: c38 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c93 :: c50:c51 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c94 :: c54:c55 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c95 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c98 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c2 :: c58:c59 -> c2 c6 :: c41:c42 -> c6 c10 :: c58:c59 -> c10 c16 :: c44:c46 -> c16 c22 :: c58:c59 -> c22 c28 :: c44:c46 -> c28 0 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c64 :: c38 -> c44:c46 -> c65:c64 U12 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c69 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U22 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c72 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U32 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c75 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U43 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c78 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U53 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c82 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U63 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c85 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U81 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil c88 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 a__zeros :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil zeros :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U11 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U12 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U21 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U22 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U31 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U32 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U41 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U42 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U43 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U51 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U52 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U53 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U61 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U62 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U63 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U71 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__length :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U81 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil nil :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__U91 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil a__take :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil Rewrite Strategy: INNERMOST ---------------------------------------- (49) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: A__U41_3 A__U51_3 A__U61_3 A__U71_2 A__U91_4 A__AND_2 A__ISNAT_1 A__ISNATILIST_1 A__ISNATILISTKIND_1 A__ISNATKIND_1 A__ISNATLIST_1 A__LENGTH_1 A__TAKE_2 MARK_1 A__U11_2 A__U21_2 A__U31_2 A__U42_2 A__U52_2 A__U62_2 (c) The following functions are completely defined: a__zeros a__U11_2 a__U12_1 a__U21_2 a__U22_1 a__U31_2 a__U32_1 a__U41_3 a__U42_2 a__U43_1 a__U51_3 a__U52_2 a__U53_1 a__U61_3 a__U62_2 a__U63_1 a__U71_2 a__U81_1 a__U91_4 a__and_2 a__isNat_1 a__isNatIList_1 a__isNatIListKind_1 a__isNatKind_1 a__isNatList_1 a__length_1 a__take_2 mark_1 Due to the following rules being added: a__zeros -> null_a__zeros [0] a__U11(v0, v1) -> null_a__U11 [0] a__U12(v0) -> null_a__U12 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0) -> null_a__U22 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U32(v0) -> null_a__U32 [0] a__U41(v0, v1, v2) -> null_a__U41 [0] a__U42(v0, v1) -> null_a__U42 [0] a__U43(v0) -> null_a__U43 [0] a__U51(v0, v1, v2) -> null_a__U51 [0] a__U52(v0, v1) -> null_a__U52 [0] a__U53(v0) -> null_a__U53 [0] a__U61(v0, v1, v2) -> null_a__U61 [0] a__U62(v0, v1) -> null_a__U62 [0] a__U63(v0) -> null_a__U63 [0] a__U71(v0, v1) -> null_a__U71 [0] a__U81(v0) -> null_a__U81 [0] a__U91(v0, v1, v2, v3) -> null_a__U91 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [0] a__isNatIList(v0) -> null_a__isNatIList [0] a__isNatIListKind(v0) -> null_a__isNatIListKind [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__isNatList(v0) -> null_a__isNatList [0] a__length(v0) -> null_a__length [0] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__zeros, null_a__U11, null_a__U12, null_a__U21, null_a__U22, null_a__U31, null_a__U32, null_a__U41, null_a__U42, null_a__U43, null_a__U51, null_a__U52, null_a__U53, null_a__U61, null_a__U62, null_a__U63, null_a__U71, null_a__U81, null_a__U91, null_a__and, null_a__isNat, null_a__isNatIList, null_a__isNatIListKind, null_a__isNatKind, null_a__isNatList, null_a__length, null_a__take, null_mark, const, const1, const2, const3, const4, const5, const6, const7, const8, const9, const10, const11, const12, const13, const14, const15, const16, const17, const18, const19 ---------------------------------------- (50) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) [1] A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) [1] A__AND(tt, z0) -> c38(MARK(z0)) [1] A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1] A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1] A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) [1] A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) [1] MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) [1] MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c73(A__ISNAT(z0)) [1] MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) [1] MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) [1] MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) [1] MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) [1] MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) [1] MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) [1] MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) [1] MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) [1] MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) [1] MARK(cons(z0, z1)) -> c95(MARK(z0)) [1] MARK(s(z0)) -> c98(MARK(z0)) [1] A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) [1] A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1] A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) [1] A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) [1] A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) [1] A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) [1] A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) [1] MARK(U12(z0)) -> c69(MARK(z0)) [1] MARK(U22(z0)) -> c72(MARK(z0)) [1] MARK(U32(z0)) -> c75(MARK(z0)) [1] MARK(U43(z0)) -> c78(MARK(z0)) [1] MARK(U53(z0)) -> c82(MARK(z0)) [1] MARK(U63(z0)) -> c85(MARK(z0)) [1] MARK(U81(z0)) -> c88(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt, z0) -> a__U12(a__isNatList(z0)) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U12(tt) -> tt [0] a__U12(z0) -> U12(z0) [0] a__U21(tt, z0) -> a__U22(a__isNat(z0)) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt) -> tt [0] a__U22(z0) -> U22(z0) [0] a__U31(tt, z0) -> a__U32(a__isNatList(z0)) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U32(tt) -> tt [0] a__U32(z0) -> U32(z0) [0] a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) [0] a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0] a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) [0] a__U42(z0, z1) -> U42(z0, z1) [0] a__U43(tt) -> tt [0] a__U43(z0) -> U43(z0) [0] a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) [0] a__U51(z0, z1, z2) -> U51(z0, z1, z2) [0] a__U52(tt, z0) -> a__U53(a__isNatList(z0)) [0] a__U52(z0, z1) -> U52(z0, z1) [0] a__U53(tt) -> tt [0] a__U53(z0) -> U53(z0) [0] a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) [0] a__U61(z0, z1, z2) -> U61(z0, z1, z2) [0] a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) [0] a__U62(z0, z1) -> U62(z0, z1) [0] a__U63(tt) -> tt [0] a__U63(z0) -> U63(z0) [0] a__U71(tt, z0) -> s(a__length(mark(z0))) [0] a__U71(z0, z1) -> U71(z0, z1) [0] a__U81(tt) -> nil [0] a__U81(z0) -> U81(z0) [0] a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__isNat(0) -> tt [0] a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) [0] a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) [0] a__isNatIList(zeros) -> tt [0] a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatIList(z0) -> isNatIList(z0) [0] a__isNatIListKind(nil) -> tt [0] a__isNatIListKind(zeros) -> tt [0] a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) [0] a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) [0] a__isNatIListKind(z0) -> isNatIListKind(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(length(z0)) -> a__isNatIListKind(z0) [0] a__isNatKind(s(z0)) -> a__isNatKind(z0) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__isNatList(nil) -> tt [0] a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatList(z0) -> isNatList(z0) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) [0] a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U12(z0)) -> a__U12(mark(z0)) [0] mark(isNatList(z0)) -> a__isNatList(z0) [0] mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0] mark(U22(z0)) -> a__U22(mark(z0)) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U32(z0)) -> a__U32(mark(z0)) [0] mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0] mark(U42(z0, z1)) -> a__U42(mark(z0), z1) [0] mark(U43(z0)) -> a__U43(mark(z0)) [0] mark(isNatIList(z0)) -> a__isNatIList(z0) [0] mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) [0] mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0] mark(U53(z0)) -> a__U53(mark(z0)) [0] mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) [0] mark(U62(z0, z1)) -> a__U62(mark(z0), z1) [0] mark(U63(z0)) -> a__U63(mark(z0)) [0] mark(U71(z0, z1)) -> a__U71(mark(z0), z1) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(U81(z0)) -> a__U81(mark(z0)) [0] mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] a__zeros -> null_a__zeros [0] a__U11(v0, v1) -> null_a__U11 [0] a__U12(v0) -> null_a__U12 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0) -> null_a__U22 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U32(v0) -> null_a__U32 [0] a__U41(v0, v1, v2) -> null_a__U41 [0] a__U42(v0, v1) -> null_a__U42 [0] a__U43(v0) -> null_a__U43 [0] a__U51(v0, v1, v2) -> null_a__U51 [0] a__U52(v0, v1) -> null_a__U52 [0] a__U53(v0) -> null_a__U53 [0] a__U61(v0, v1, v2) -> null_a__U61 [0] a__U62(v0, v1) -> null_a__U62 [0] a__U63(v0) -> null_a__U63 [0] a__U71(v0, v1) -> null_a__U71 [0] a__U81(v0) -> null_a__U81 [0] a__U91(v0, v1, v2, v3) -> null_a__U91 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [0] a__isNatIList(v0) -> null_a__isNatIList [0] a__isNatIListKind(v0) -> null_a__isNatIListKind [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__isNatList(v0) -> null_a__isNatList [0] a__length(v0) -> null_a__length [0] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__U41 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c14 tt :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c14 :: c16 -> c41:c42 -> c14 A__U42 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c16 a__isNat :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark A__ISNAT :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c41:c42 A__U51 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c20 c20 :: c22 -> c41:c42 -> c20 A__U52 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c22 A__U61 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c26 c26 :: c28 -> c41:c42 -> c26 A__U62 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c28 A__U71 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c32 c32 :: c62 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c32 A__LENGTH :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c62 mark :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark MARK :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 A__U91 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c36 c36 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c36 A__AND :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c38 c38 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c38 length :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c41 :: c2 -> c50:c51 -> c41:c42 A__U11 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c2 a__isNatIListKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark A__ISNATILISTKIND :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c50:c51 s :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c42 :: c6 -> c54:c55 -> c41:c42 A__U21 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c6 a__isNatKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark A__ISNATKIND :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c54:c55 A__ISNATILIST :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c44:c46 c44 :: c10 -> c50:c51 -> c44:c46 A__U31 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c10 cons :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c46 :: c14 -> c38 -> c54:c55 -> c44:c46 a__and :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark isNatIListKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c50 :: c38 -> c54:c55 -> c50:c51 take :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c51 :: c38 -> c54:c55 -> c50:c51 c54 :: c50:c51 -> c54:c55 c55 :: c54:c55 -> c54:c55 A__ISNATLIST :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c58:c59 c58 :: c20 -> c38 -> c54:c55 -> c58:c59 c59 :: c26 -> c38 -> c54:c55 -> c58:c59 c62 :: c32 -> c38 -> c38 -> c58:c59 -> c62 a__isNatList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark and :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark isNat :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark isNatKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark A__TAKE :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c65:c64 c65 :: c36 -> c38 -> c38 -> c44:c46 -> c65:c64 a__isNatIList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark U11 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c68 :: c2 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 isNatList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c70 :: c58:c59 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U21 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c71 :: c6 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c73 :: c41:c42 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U31 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c74 :: c10 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U41 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c76 :: c14 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U42 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c77 :: c16 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 isNatIList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c79 :: c44:c46 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U51 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c80 :: c20 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U52 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c81 :: c22 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U61 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c83 :: c26 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U62 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c84 :: c28 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U71 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c86 :: c32 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c87 :: c62 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U91 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c89 :: c36 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c90 :: c65:c64 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c91 :: c65:c64 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c92 :: c38 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c93 :: c50:c51 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c94 :: c54:c55 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c95 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c98 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c2 :: c58:c59 -> c2 c6 :: c41:c42 -> c6 c10 :: c58:c59 -> c10 c16 :: c44:c46 -> c16 c22 :: c58:c59 -> c22 c28 :: c44:c46 -> c28 0 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c64 :: c38 -> c44:c46 -> c65:c64 U12 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c69 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U22 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c72 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U32 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c75 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U43 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> 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tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> 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tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> 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tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark a__U11 :: 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tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> 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tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> 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---------------------------------------- (51) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (52) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U41(tt, 0, z1) -> c14(A__U42(tt, z1), A__ISNAT(0)) [1] A__U41(tt, length(z0'), z1) -> c14(A__U42(a__U11(a__isNatIListKind(z0'), z0'), z1), A__ISNAT(length(z0'))) [1] A__U41(tt, s(z0''), z1) -> c14(A__U42(a__U21(a__isNatKind(z0''), z0''), z1), A__ISNAT(s(z0''))) [1] A__U41(tt, z0, z1) -> c14(A__U42(isNat(z0), z1), A__ISNAT(z0)) [1] A__U41(tt, z0, z1) -> c14(A__U42(null_a__isNat, z1), A__ISNAT(z0)) [1] A__U51(tt, 0, z1) -> c20(A__U52(tt, z1), A__ISNAT(0)) [1] A__U51(tt, length(z01), z1) -> c20(A__U52(a__U11(a__isNatIListKind(z01), z01), z1), A__ISNAT(length(z01))) [1] A__U51(tt, s(z02), z1) -> c20(A__U52(a__U21(a__isNatKind(z02), z02), z1), A__ISNAT(s(z02))) [1] A__U51(tt, z0, z1) -> c20(A__U52(isNat(z0), z1), A__ISNAT(z0)) [1] A__U51(tt, z0, z1) -> c20(A__U52(null_a__isNat, z1), A__ISNAT(z0)) [1] A__U61(tt, 0, z1) -> c26(A__U62(tt, z1), A__ISNAT(0)) [1] A__U61(tt, length(z03), z1) -> c26(A__U62(a__U11(a__isNatIListKind(z03), z03), z1), A__ISNAT(length(z03))) [1] A__U61(tt, s(z04), z1) -> c26(A__U62(a__U21(a__isNatKind(z04), z04), z1), A__ISNAT(s(z04))) [1] A__U61(tt, z0, z1) -> c26(A__U62(isNat(z0), z1), A__ISNAT(z0)) [1] A__U61(tt, z0, z1) -> c26(A__U62(null_a__isNat, z1), A__ISNAT(z0)) [1] A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) [1] A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) [1] A__AND(tt, z0) -> c38(MARK(z0)) [1] A__ISNAT(length(nil)) -> c41(A__U11(tt, nil), A__ISNATILISTKIND(nil)) [1] A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros), A__ISNATILISTKIND(zeros)) [1] A__ISNAT(length(cons(z033, z113))) -> c41(A__U11(a__and(a__isNatKind(z033), isNatIListKind(z113)), cons(z033, z113)), A__ISNATILISTKIND(cons(z033, z113))) [1] A__ISNAT(length(take(z034, z114))) -> c41(A__U11(a__and(a__isNatKind(z034), isNatIListKind(z114)), take(z034, z114)), A__ISNATILISTKIND(take(z034, z114))) [1] A__ISNAT(length(z0)) -> c41(A__U11(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1] A__ISNAT(length(z0)) -> c41(A__U11(null_a__isNatIListKind, z0), A__ISNATILISTKIND(z0)) [1] A__ISNAT(s(0)) -> c42(A__U21(tt, 0), A__ISNATKIND(0)) [1] A__ISNAT(s(length(z035))) -> c42(A__U21(a__isNatIListKind(z035), length(z035)), A__ISNATKIND(length(z035))) [1] A__ISNAT(s(s(z036))) -> c42(A__U21(a__isNatKind(z036), s(z036)), A__ISNATKIND(s(z036))) [1] A__ISNAT(s(z0)) -> c42(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNAT(s(z0)) -> c42(A__U21(null_a__isNatKind, z0), A__ISNATKIND(z0)) [1] A__ISNATILIST(nil) -> c44(A__U31(tt, nil), A__ISNATILISTKIND(nil)) [1] A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros), A__ISNATILISTKIND(zeros)) [1] A__ISNATILIST(cons(z037, z115)) -> c44(A__U31(a__and(a__isNatKind(z037), isNatIListKind(z115)), cons(z037, z115)), A__ISNATILISTKIND(cons(z037, z115))) [1] A__ISNATILIST(take(z038, z116)) -> c44(A__U31(a__and(a__isNatKind(z038), isNatIListKind(z116)), take(z038, z116)), A__ISNATILISTKIND(take(z038, z116))) [1] A__ISNATILIST(z0) -> c44(A__U31(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1] A__ISNATILIST(z0) -> c44(A__U31(null_a__isNatIListKind, z0), A__ISNATILISTKIND(z0)) [1] A__ISNATILIST(cons(0, z1)) -> c46(A__U41(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATILIST(cons(0, z1)) -> c46(A__U41(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(isNatKind(0), isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATILIST(cons(0, z1)) -> c46(A__U41(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATILIST(cons(length(z039), z1)) -> c46(A__U41(a__and(a__isNatIListKind(z039), isNatIListKind(z1)), length(z039), z1), A__AND(a__isNatIListKind(z039), isNatIListKind(z1)), A__ISNATKIND(length(z039))) [1] A__ISNATILIST(cons(length(z039), z1)) -> c46(A__U41(a__and(a__isNatIListKind(z039), isNatIListKind(z1)), length(z039), z1), A__AND(isNatKind(length(z039)), isNatIListKind(z1)), A__ISNATKIND(length(z039))) [1] A__ISNATILIST(cons(length(z039), z1)) -> c46(A__U41(a__and(a__isNatIListKind(z039), isNatIListKind(z1)), length(z039), z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(length(z039))) [1] A__ISNATILIST(cons(s(z040), z1)) -> c46(A__U41(a__and(a__isNatKind(z040), isNatIListKind(z1)), s(z040), z1), A__AND(a__isNatKind(z040), isNatIListKind(z1)), A__ISNATKIND(s(z040))) [1] A__ISNATILIST(cons(s(z040), z1)) -> c46(A__U41(a__and(a__isNatKind(z040), isNatIListKind(z1)), s(z040), z1), A__AND(isNatKind(s(z040)), isNatIListKind(z1)), A__ISNATKIND(s(z040))) [1] A__ISNATILIST(cons(s(z040), z1)) -> c46(A__U41(a__and(a__isNatKind(z040), isNatIListKind(z1)), s(z040), z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(s(z040))) [1] A__ISNATILIST(cons(0, z1)) -> c46(A__U41(a__and(isNatKind(0), isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATILIST(cons(length(z041), z1)) -> c46(A__U41(a__and(isNatKind(length(z041)), isNatIListKind(z1)), length(z041), z1), A__AND(a__isNatIListKind(z041), isNatIListKind(z1)), A__ISNATKIND(length(z041))) [1] A__ISNATILIST(cons(s(z042), z1)) -> c46(A__U41(a__and(isNatKind(s(z042)), isNatIListKind(z1)), s(z042), z1), A__AND(a__isNatKind(z042), isNatIListKind(z1)), A__ISNATKIND(s(z042))) [1] A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILIST(cons(0, z1)) -> c46(A__U41(a__and(null_a__isNatKind, isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATILIST(cons(length(z043), z1)) -> c46(A__U41(a__and(null_a__isNatKind, isNatIListKind(z1)), length(z043), z1), A__AND(a__isNatIListKind(z043), isNatIListKind(z1)), A__ISNATKIND(length(z043))) [1] A__ISNATILIST(cons(s(z044), z1)) -> c46(A__U41(a__and(null_a__isNatKind, isNatIListKind(z1)), s(z044), z1), A__AND(a__isNatKind(z044), isNatIListKind(z1)), A__ISNATKIND(s(z044))) [1] A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1), A__AND(isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILISTKIND(cons(0, z1)) -> c50(A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATILISTKIND(cons(length(z045), z1)) -> c50(A__AND(a__isNatIListKind(z045), isNatIListKind(z1)), A__ISNATKIND(length(z045))) [1] A__ISNATILISTKIND(cons(s(z046), z1)) -> c50(A__AND(a__isNatKind(z046), isNatIListKind(z1)), A__ISNATKIND(s(z046))) [1] A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILISTKIND(take(0, z1)) -> c51(A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATILISTKIND(take(length(z047), z1)) -> c51(A__AND(a__isNatIListKind(z047), isNatIListKind(z1)), A__ISNATKIND(length(z047))) [1] A__ISNATILISTKIND(take(s(z048), z1)) -> c51(A__AND(a__isNatKind(z048), isNatIListKind(z1)), A__ISNATKIND(s(z048))) [1] A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) [1] A__ISNATLIST(cons(0, z1)) -> c58(A__U51(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATLIST(cons(0, z1)) -> c58(A__U51(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(isNatKind(0), isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATLIST(cons(0, z1)) -> c58(A__U51(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATLIST(cons(length(z049), z1)) -> c58(A__U51(a__and(a__isNatIListKind(z049), isNatIListKind(z1)), length(z049), z1), A__AND(a__isNatIListKind(z049), isNatIListKind(z1)), A__ISNATKIND(length(z049))) [1] A__ISNATLIST(cons(length(z049), z1)) -> c58(A__U51(a__and(a__isNatIListKind(z049), isNatIListKind(z1)), length(z049), z1), A__AND(isNatKind(length(z049)), isNatIListKind(z1)), A__ISNATKIND(length(z049))) [1] A__ISNATLIST(cons(length(z049), z1)) -> c58(A__U51(a__and(a__isNatIListKind(z049), isNatIListKind(z1)), length(z049), z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(length(z049))) [1] A__ISNATLIST(cons(s(z050), z1)) -> c58(A__U51(a__and(a__isNatKind(z050), isNatIListKind(z1)), s(z050), z1), A__AND(a__isNatKind(z050), isNatIListKind(z1)), A__ISNATKIND(s(z050))) [1] A__ISNATLIST(cons(s(z050), z1)) -> c58(A__U51(a__and(a__isNatKind(z050), isNatIListKind(z1)), s(z050), z1), A__AND(isNatKind(s(z050)), isNatIListKind(z1)), A__ISNATKIND(s(z050))) [1] A__ISNATLIST(cons(s(z050), z1)) -> c58(A__U51(a__and(a__isNatKind(z050), isNatIListKind(z1)), s(z050), z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(s(z050))) [1] A__ISNATLIST(cons(0, z1)) -> c58(A__U51(a__and(isNatKind(0), isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATLIST(cons(length(z051), z1)) -> c58(A__U51(a__and(isNatKind(length(z051)), isNatIListKind(z1)), length(z051), z1), A__AND(a__isNatIListKind(z051), isNatIListKind(z1)), A__ISNATKIND(length(z051))) [1] A__ISNATLIST(cons(s(z052), z1)) -> c58(A__U51(a__and(isNatKind(s(z052)), isNatIListKind(z1)), s(z052), z1), A__AND(a__isNatKind(z052), isNatIListKind(z1)), A__ISNATKIND(s(z052))) [1] A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATLIST(cons(0, z1)) -> c58(A__U51(a__and(null_a__isNatKind, isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATLIST(cons(length(z053), z1)) -> c58(A__U51(a__and(null_a__isNatKind, isNatIListKind(z1)), length(z053), z1), A__AND(a__isNatIListKind(z053), isNatIListKind(z1)), A__ISNATKIND(length(z053))) [1] A__ISNATLIST(cons(s(z054), z1)) -> c58(A__U51(a__and(null_a__isNatKind, isNatIListKind(z1)), s(z054), z1), A__AND(a__isNatKind(z054), isNatIListKind(z1)), A__ISNATKIND(s(z054))) [1] A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1), A__AND(isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATLIST(take(0, z1)) -> c59(A__U61(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATLIST(take(0, z1)) -> c59(A__U61(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(isNatKind(0), isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATLIST(take(0, z1)) -> c59(A__U61(a__and(tt, isNatIListKind(z1)), 0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATLIST(take(length(z055), z1)) -> c59(A__U61(a__and(a__isNatIListKind(z055), isNatIListKind(z1)), length(z055), z1), A__AND(a__isNatIListKind(z055), isNatIListKind(z1)), A__ISNATKIND(length(z055))) [1] A__ISNATLIST(take(length(z055), z1)) -> c59(A__U61(a__and(a__isNatIListKind(z055), isNatIListKind(z1)), length(z055), z1), A__AND(isNatKind(length(z055)), isNatIListKind(z1)), A__ISNATKIND(length(z055))) [1] A__ISNATLIST(take(length(z055), z1)) -> c59(A__U61(a__and(a__isNatIListKind(z055), isNatIListKind(z1)), length(z055), z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(length(z055))) [1] A__ISNATLIST(take(s(z056), z1)) -> c59(A__U61(a__and(a__isNatKind(z056), isNatIListKind(z1)), s(z056), z1), A__AND(a__isNatKind(z056), isNatIListKind(z1)), A__ISNATKIND(s(z056))) [1] A__ISNATLIST(take(s(z056), z1)) -> c59(A__U61(a__and(a__isNatKind(z056), isNatIListKind(z1)), s(z056), z1), A__AND(isNatKind(s(z056)), isNatIListKind(z1)), A__ISNATKIND(s(z056))) [1] A__ISNATLIST(take(s(z056), z1)) -> c59(A__U61(a__and(a__isNatKind(z056), isNatIListKind(z1)), s(z056), z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(s(z056))) [1] A__ISNATLIST(take(0, z1)) -> c59(A__U61(a__and(isNatKind(0), isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATLIST(take(length(z057), z1)) -> c59(A__U61(a__and(isNatKind(length(z057)), isNatIListKind(z1)), length(z057), z1), A__AND(a__isNatIListKind(z057), isNatIListKind(z1)), A__ISNATKIND(length(z057))) [1] A__ISNATLIST(take(s(z058), z1)) -> c59(A__U61(a__and(isNatKind(s(z058)), isNatIListKind(z1)), s(z058), z1), A__AND(a__isNatKind(z058), isNatIListKind(z1)), A__ISNATKIND(s(z058))) [1] A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATLIST(take(0, z1)) -> c59(A__U61(a__and(null_a__isNatKind, isNatIListKind(z1)), 0, z1), A__AND(tt, isNatIListKind(z1)), A__ISNATKIND(0)) [1] A__ISNATLIST(take(length(z059), z1)) -> c59(A__U61(a__and(null_a__isNatKind, isNatIListKind(z1)), length(z059), z1), A__AND(a__isNatIListKind(z059), isNatIListKind(z1)), A__ISNATKIND(length(z059))) [1] A__ISNATLIST(take(s(z060), z1)) -> c59(A__U61(a__and(null_a__isNatKind, isNatIListKind(z1)), s(z060), z1), A__AND(a__isNatKind(z060), isNatIListKind(z1)), A__ISNATKIND(s(z060))) [1] A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1), A__AND(isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1), A__AND(null_a__isNatKind, isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) [1] MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) [1] MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c73(A__ISNAT(z0)) [1] MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) [1] MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) [1] MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) [1] MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) [1] MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) [1] MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) [1] MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) [1] MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) [1] MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) [1] MARK(cons(z0, z1)) -> c95(MARK(z0)) [1] MARK(s(z0)) -> c98(MARK(z0)) [1] A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) [1] A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1] A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) [1] A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) [1] A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) [1] A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) [1] A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) [1] A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) [1] A__TAKE(0, cons(z02356, z11178)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z02356), isNatIListKind(z11178)), z02356, z11178), isNatIListKind(cons(z02356, z11178))), A__ISNATILIST(cons(z02356, z11178))) [1] A__TAKE(0, z0) -> c64(A__AND(isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) [1] A__TAKE(0, z0) -> c64(A__AND(null_a__isNatIList, isNatIListKind(z0)), A__ISNATILIST(z0)) [1] MARK(U12(z0)) -> c69(MARK(z0)) [1] MARK(U22(z0)) -> c72(MARK(z0)) [1] MARK(U32(z0)) -> c75(MARK(z0)) [1] MARK(U43(z0)) -> c78(MARK(z0)) [1] MARK(U53(z0)) -> c82(MARK(z0)) [1] MARK(U63(z0)) -> c85(MARK(z0)) [1] MARK(U81(z0)) -> c88(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt, nil) -> a__U12(tt) [0] a__U11(tt, cons(z02357, z11179)) -> a__U12(a__U51(a__and(a__isNatKind(z02357), isNatIListKind(z11179)), z02357, z11179)) [0] a__U11(tt, take(z02358, z11180)) -> a__U12(a__U61(a__and(a__isNatKind(z02358), isNatIListKind(z11180)), z02358, z11180)) [0] a__U11(tt, z0) -> a__U12(isNatList(z0)) [0] a__U11(tt, z0) -> a__U12(null_a__isNatList) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U12(tt) -> tt [0] a__U12(z0) -> U12(z0) [0] a__U21(tt, 0) -> a__U22(tt) [0] a__U21(tt, length(z02359)) -> a__U22(a__U11(a__isNatIListKind(z02359), z02359)) [0] a__U21(tt, s(z02360)) -> a__U22(a__U21(a__isNatKind(z02360), z02360)) [0] a__U21(tt, z0) -> a__U22(isNat(z0)) [0] a__U21(tt, z0) -> a__U22(null_a__isNat) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt) -> tt [0] a__U22(z0) -> U22(z0) [0] a__U31(tt, nil) -> a__U32(tt) [0] a__U31(tt, cons(z02361, z11181)) -> a__U32(a__U51(a__and(a__isNatKind(z02361), isNatIListKind(z11181)), z02361, z11181)) [0] a__U31(tt, take(z02362, z11182)) -> a__U32(a__U61(a__and(a__isNatKind(z02362), isNatIListKind(z11182)), z02362, z11182)) [0] a__U31(tt, z0) -> a__U32(isNatList(z0)) [0] a__U31(tt, z0) -> a__U32(null_a__isNatList) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U32(tt) -> tt [0] a__U32(z0) -> U32(z0) [0] a__U41(tt, 0, z1) -> a__U42(tt, z1) [0] a__U41(tt, length(z02363), z1) -> a__U42(a__U11(a__isNatIListKind(z02363), z02363), z1) [0] a__U41(tt, s(z02364), z1) -> a__U42(a__U21(a__isNatKind(z02364), z02364), z1) [0] a__U41(tt, z0, z1) -> a__U42(isNat(z0), z1) [0] a__U41(tt, z0, z1) -> a__U42(null_a__isNat, z1) [0] a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0] a__U42(tt, z0) -> a__U43(a__U31(a__isNatIListKind(z0), z0)) [0] a__U42(tt, zeros) -> a__U43(tt) [0] a__U42(tt, cons(z02365, z11183)) -> a__U43(a__U41(a__and(a__isNatKind(z02365), isNatIListKind(z11183)), z02365, z11183)) [0] a__U42(tt, z0) -> a__U43(isNatIList(z0)) [0] a__U42(tt, z0) -> a__U43(null_a__isNatIList) [0] a__U42(z0, z1) -> U42(z0, z1) [0] a__U43(tt) -> tt [0] a__U43(z0) -> U43(z0) [0] a__U51(tt, 0, z1) -> a__U52(tt, z1) [0] a__U51(tt, length(z02366), z1) -> a__U52(a__U11(a__isNatIListKind(z02366), z02366), z1) [0] a__U51(tt, s(z02367), z1) -> a__U52(a__U21(a__isNatKind(z02367), z02367), z1) [0] a__U51(tt, z0, z1) -> a__U52(isNat(z0), z1) [0] a__U51(tt, z0, z1) -> a__U52(null_a__isNat, z1) [0] a__U51(z0, z1, z2) -> U51(z0, z1, z2) [0] a__U52(tt, nil) -> a__U53(tt) [0] a__U52(tt, cons(z02368, z11184)) -> a__U53(a__U51(a__and(a__isNatKind(z02368), isNatIListKind(z11184)), z02368, z11184)) [0] a__U52(tt, take(z02369, z11185)) -> a__U53(a__U61(a__and(a__isNatKind(z02369), isNatIListKind(z11185)), z02369, z11185)) [0] a__U52(tt, z0) -> a__U53(isNatList(z0)) [0] a__U52(tt, z0) -> a__U53(null_a__isNatList) [0] a__U52(z0, z1) -> U52(z0, z1) [0] a__U53(tt) -> tt [0] a__U53(z0) -> U53(z0) [0] a__U61(tt, 0, z1) -> a__U62(tt, z1) [0] a__U61(tt, length(z02370), z1) -> a__U62(a__U11(a__isNatIListKind(z02370), z02370), z1) [0] a__U61(tt, s(z02371), z1) -> a__U62(a__U21(a__isNatKind(z02371), z02371), z1) [0] a__U61(tt, z0, z1) -> a__U62(isNat(z0), z1) [0] a__U61(tt, z0, z1) -> a__U62(null_a__isNat, z1) [0] a__U61(z0, z1, z2) -> U61(z0, z1, z2) [0] a__U62(tt, z0) -> a__U63(a__U31(a__isNatIListKind(z0), z0)) [0] a__U62(tt, zeros) -> a__U63(tt) [0] a__U62(tt, cons(z02372, z11186)) -> a__U63(a__U41(a__and(a__isNatKind(z02372), isNatIListKind(z11186)), z02372, z11186)) [0] a__U62(tt, z0) -> a__U63(isNatIList(z0)) [0] a__U62(tt, z0) -> a__U63(null_a__isNatIList) [0] a__U62(z0, z1) -> U62(z0, z1) [0] a__U63(tt) -> tt [0] a__U63(z0) -> U63(z0) [0] a__U71(tt, z0) -> s(a__length(mark(z0))) [0] a__U71(z0, z1) -> U71(z0, z1) [0] a__U81(tt) -> nil [0] a__U81(z0) -> U81(z0) [0] a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__isNat(0) -> tt [0] a__isNat(length(nil)) -> a__U11(tt, nil) [0] a__isNat(length(zeros)) -> a__U11(tt, zeros) [0] a__isNat(length(cons(z02401, z11201))) -> a__U11(a__and(a__isNatKind(z02401), isNatIListKind(z11201)), cons(z02401, z11201)) [0] a__isNat(length(take(z02402, z11202))) -> a__U11(a__and(a__isNatKind(z02402), isNatIListKind(z11202)), take(z02402, z11202)) [0] a__isNat(length(z0)) -> a__U11(isNatIListKind(z0), z0) [0] a__isNat(length(z0)) -> a__U11(null_a__isNatIListKind, z0) [0] a__isNat(s(0)) -> a__U21(tt, 0) [0] a__isNat(s(length(z02403))) -> a__U21(a__isNatIListKind(z02403), length(z02403)) [0] a__isNat(s(s(z02404))) -> a__U21(a__isNatKind(z02404), s(z02404)) [0] a__isNat(s(z0)) -> a__U21(isNatKind(z0), z0) [0] a__isNat(s(z0)) -> a__U21(null_a__isNatKind, z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatIList(nil) -> a__U31(tt, nil) [0] a__isNatIList(zeros) -> a__U31(tt, zeros) [0] a__isNatIList(cons(z02405, z11203)) -> a__U31(a__and(a__isNatKind(z02405), isNatIListKind(z11203)), cons(z02405, z11203)) [0] a__isNatIList(take(z02406, z11204)) -> a__U31(a__and(a__isNatKind(z02406), isNatIListKind(z11204)), take(z02406, z11204)) [0] a__isNatIList(z0) -> a__U31(isNatIListKind(z0), z0) [0] a__isNatIList(z0) -> a__U31(null_a__isNatIListKind, z0) [0] a__isNatIList(zeros) -> tt [0] a__isNatIList(cons(0, z1)) -> a__U41(a__and(tt, isNatIListKind(z1)), 0, z1) [0] a__isNatIList(cons(length(z02407), z1)) -> a__U41(a__and(a__isNatIListKind(z02407), isNatIListKind(z1)), length(z02407), z1) [0] a__isNatIList(cons(s(z02408), z1)) -> a__U41(a__and(a__isNatKind(z02408), isNatIListKind(z1)), s(z02408), z1) [0] a__isNatIList(cons(z0, z1)) -> a__U41(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatIList(cons(z0, z1)) -> a__U41(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1) [0] a__isNatIList(z0) -> isNatIList(z0) [0] a__isNatIListKind(nil) -> tt [0] a__isNatIListKind(zeros) -> tt [0] a__isNatIListKind(cons(0, z1)) -> a__and(tt, isNatIListKind(z1)) [0] a__isNatIListKind(cons(length(z02409), z1)) -> a__and(a__isNatIListKind(z02409), isNatIListKind(z1)) [0] a__isNatIListKind(cons(s(z02410), z1)) -> a__and(a__isNatKind(z02410), isNatIListKind(z1)) [0] a__isNatIListKind(cons(z0, z1)) -> a__and(isNatKind(z0), isNatIListKind(z1)) [0] a__isNatIListKind(cons(z0, z1)) -> a__and(null_a__isNatKind, isNatIListKind(z1)) [0] a__isNatIListKind(take(0, z1)) -> a__and(tt, isNatIListKind(z1)) [0] a__isNatIListKind(take(length(z02411), z1)) -> a__and(a__isNatIListKind(z02411), isNatIListKind(z1)) [0] a__isNatIListKind(take(s(z02412), z1)) -> a__and(a__isNatKind(z02412), isNatIListKind(z1)) [0] a__isNatIListKind(take(z0, z1)) -> a__and(isNatKind(z0), isNatIListKind(z1)) [0] a__isNatIListKind(take(z0, z1)) -> a__and(null_a__isNatKind, isNatIListKind(z1)) [0] a__isNatIListKind(z0) -> isNatIListKind(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(length(z0)) -> a__isNatIListKind(z0) [0] a__isNatKind(s(z0)) -> a__isNatKind(z0) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__isNatList(nil) -> tt [0] a__isNatList(cons(0, z1)) -> a__U51(a__and(tt, isNatIListKind(z1)), 0, z1) [0] a__isNatList(cons(length(z02413), z1)) -> a__U51(a__and(a__isNatIListKind(z02413), isNatIListKind(z1)), length(z02413), z1) [0] a__isNatList(cons(s(z02414), z1)) -> a__U51(a__and(a__isNatKind(z02414), isNatIListKind(z1)), s(z02414), z1) [0] a__isNatList(cons(z0, z1)) -> a__U51(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatList(cons(z0, z1)) -> a__U51(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1) [0] a__isNatList(take(0, z1)) -> a__U61(a__and(tt, isNatIListKind(z1)), 0, z1) [0] a__isNatList(take(length(z02415), z1)) -> a__U61(a__and(a__isNatIListKind(z02415), isNatIListKind(z1)), length(z02415), z1) [0] a__isNatList(take(s(z02416), z1)) -> a__U61(a__and(a__isNatKind(z02416), isNatIListKind(z1)), s(z02416), z1) [0] a__isNatList(take(z0, z1)) -> a__U61(a__and(isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatList(take(z0, z1)) -> a__U61(a__and(null_a__isNatKind, isNatIListKind(z1)), z0, z1) [0] a__isNatList(z0) -> isNatList(z0) [0] a__length(nil) -> 0 [0] a__length(cons(z0, nil)) -> a__U71(a__and(a__and(tt, isNatIListKind(nil)), and(isNat(z0), isNatKind(z0))), nil) [0] a__length(cons(z0, cons(z02417, z11205))) -> a__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z02417), isNatIListKind(z11205)), z02417, z11205), isNatIListKind(cons(z02417, z11205))), and(isNat(z0), isNatKind(z0))), cons(z02417, z11205)) [0] a__length(cons(z0, take(z02418, z11206))) -> a__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z02418), isNatIListKind(z11206)), z02418, z11206), isNatIListKind(take(z02418, z11206))), and(isNat(z0), isNatKind(z0))), take(z02418, z11206)) [0] a__length(cons(z0, z1)) -> a__U71(a__and(a__and(isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) [0] a__length(cons(z0, z1)) -> a__U71(a__and(a__and(null_a__isNatList, isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> a__U81(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0))) [0] a__take(0, zeros) -> a__U81(a__and(tt, isNatIListKind(zeros))) [0] a__take(0, cons(z02419, z11207)) -> a__U81(a__and(a__U41(a__and(a__isNatKind(z02419), isNatIListKind(z11207)), z02419, z11207), isNatIListKind(cons(z02419, z11207)))) [0] a__take(0, z0) -> a__U81(a__and(isNatIList(z0), isNatIListKind(z0))) [0] a__take(0, z0) -> a__U81(a__and(null_a__isNatIList, isNatIListKind(z0))) [0] a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__U31(a__isNatIListKind(z2), z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) [0] a__take(s(z0), cons(z1, zeros)) -> a__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), zeros, z0, z1) [0] a__take(s(z0), cons(z1, cons(z02420, z11208))) -> a__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z02420), isNatIListKind(z11208)), z02420, z11208), isNatIListKind(cons(z02420, z11208))), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), cons(z02420, z11208), z0, z1) [0] a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) [0] a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(null_a__isNatIList, isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U12(z0)) -> a__U12(mark(z0)) [0] mark(isNatList(z0)) -> a__isNatList(z0) [0] mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0] mark(U22(z0)) -> a__U22(mark(z0)) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U32(z0)) -> a__U32(mark(z0)) [0] mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0] mark(U42(z0, z1)) -> a__U42(mark(z0), z1) [0] mark(U43(z0)) -> a__U43(mark(z0)) [0] mark(isNatIList(z0)) -> a__isNatIList(z0) [0] mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) [0] mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0] mark(U53(z0)) -> a__U53(mark(z0)) [0] mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) [0] mark(U62(z0, z1)) -> a__U62(mark(z0), z1) [0] mark(U63(z0)) -> a__U63(mark(z0)) [0] mark(U71(z0, z1)) -> a__U71(mark(z0), z1) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(U81(z0)) -> a__U81(mark(z0)) [0] mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] a__zeros -> null_a__zeros [0] a__U11(v0, v1) -> null_a__U11 [0] a__U12(v0) -> null_a__U12 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0) -> null_a__U22 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U32(v0) -> null_a__U32 [0] a__U41(v0, v1, v2) -> null_a__U41 [0] a__U42(v0, v1) -> null_a__U42 [0] a__U43(v0) -> null_a__U43 [0] a__U51(v0, v1, v2) -> null_a__U51 [0] a__U52(v0, v1) -> null_a__U52 [0] a__U53(v0) -> null_a__U53 [0] a__U61(v0, v1, v2) -> null_a__U61 [0] a__U62(v0, v1) -> null_a__U62 [0] a__U63(v0) -> null_a__U63 [0] a__U71(v0, v1) -> null_a__U71 [0] a__U81(v0) -> null_a__U81 [0] a__U91(v0, v1, v2, v3) -> null_a__U91 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [0] a__isNatIList(v0) -> null_a__isNatIList [0] a__isNatIListKind(v0) -> null_a__isNatIListKind [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__isNatList(v0) -> null_a__isNatList [0] a__length(v0) -> null_a__length [0] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__U41 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c14 tt :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c14 :: c16 -> c41:c42 -> c14 A__U42 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c16 a__isNat :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark A__ISNAT :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c41:c42 A__U51 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c20 c20 :: c22 -> c41:c42 -> c20 A__U52 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c22 A__U61 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c26 c26 :: c28 -> c41:c42 -> c26 A__U62 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c28 A__U71 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c32 c32 :: c62 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c32 A__LENGTH :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c62 mark :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark MARK :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 A__U91 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c36 c36 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c36 A__AND :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c38 c38 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c38 length :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c41 :: c2 -> c50:c51 -> c41:c42 A__U11 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c2 a__isNatIListKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark A__ISNATILISTKIND :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c50:c51 s :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c42 :: c6 -> c54:c55 -> c41:c42 A__U21 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c6 a__isNatKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark A__ISNATKIND :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c54:c55 A__ISNATILIST :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c44:c46 c44 :: c10 -> c50:c51 -> c44:c46 A__U31 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c10 cons :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c46 :: c14 -> c38 -> c54:c55 -> c44:c46 a__and :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark isNatIListKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c50 :: c38 -> c54:c55 -> c50:c51 take :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c51 :: c38 -> c54:c55 -> c50:c51 c54 :: c50:c51 -> c54:c55 c55 :: c54:c55 -> c54:c55 A__ISNATLIST :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c58:c59 c58 :: c20 -> c38 -> c54:c55 -> c58:c59 c59 :: c26 -> c38 -> c54:c55 -> c58:c59 c62 :: c32 -> c38 -> c38 -> c58:c59 -> c62 a__isNatList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark and :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark isNat :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark isNatKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark A__TAKE :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c65:c64 c65 :: c36 -> c38 -> c38 -> c44:c46 -> c65:c64 a__isNatIList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark U11 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c68 :: c2 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 isNatList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c70 :: c58:c59 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U21 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c71 :: c6 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c73 :: c41:c42 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U31 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c74 :: c10 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U41 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c76 :: c14 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U42 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c77 :: c16 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 isNatIList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c79 :: c44:c46 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U51 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c80 :: c20 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U52 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c81 :: c22 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U61 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c83 :: c26 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U62 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c84 :: c28 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U71 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c86 :: c32 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c87 :: c62 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U91 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c89 :: c36 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c90 :: c65:c64 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c91 :: c65:c64 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c92 :: c38 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c93 :: c50:c51 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c94 :: c54:c55 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c95 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c98 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 c2 :: c58:c59 -> c2 c6 :: c41:c42 -> c6 c10 :: c58:c59 -> c10 c16 :: c44:c46 -> c16 c22 :: c58:c59 -> c22 c28 :: c44:c46 -> c28 0 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c64 :: c38 -> c44:c46 -> c65:c64 U12 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c69 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U22 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c72 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U32 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c75 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U43 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c78 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U53 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c82 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 U63 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> 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tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U63 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U71 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U81 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U91 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__and :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__isNat :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__isNatIList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__isNatIListKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__isNatKind :: 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tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__length :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__take :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_mark :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark const :: c14 const1 :: c16 const2 :: c41:c42 const3 :: c20 const4 :: c22 const5 :: c26 const6 :: c28 const7 :: c32 const8 :: c62 const9 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88 const10 :: c36 const11 :: c38 const12 :: c2 const13 :: c50:c51 const14 :: c6 const15 :: c54:c55 const16 :: c44:c46 const17 :: c10 const18 :: c58:c59 const19 :: c65:c64 Rewrite Strategy: INNERMOST ---------------------------------------- (53) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 2 0 => 0 zeros => 3 nil => 1 null_a__zeros => 0 null_a__U11 => 0 null_a__U12 => 0 null_a__U21 => 0 null_a__U22 => 0 null_a__U31 => 0 null_a__U32 => 0 null_a__U41 => 0 null_a__U42 => 0 null_a__U43 => 0 null_a__U51 => 0 null_a__U52 => 0 null_a__U53 => 0 null_a__U61 => 0 null_a__U62 => 0 null_a__U63 => 0 null_a__U71 => 0 null_a__U81 => 0 null_a__U91 => 0 null_a__and => 0 null_a__isNat => 0 null_a__isNatIList => 0 null_a__isNatIListKind => 0 null_a__isNatKind => 0 null_a__isNatList => 0 null_a__length => 0 null_a__take => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 const3 => 0 const4 => 0 const5 => 0 const6 => 0 const7 => 0 const8 => 0 const9 => 0 const10 => 0 const11 => 0 const12 => 0 const13 => 0 const14 => 0 const15 => 0 const16 => 0 const17 => 0 const18 => 0 const19 => 0 ---------------------------------------- (54) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z036), 1 + z036) + A__ISNATKIND(1 + z036) :|: z036 >= 0, z = 1 + (1 + z036) A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatIListKind(z035), 1 + z035) + A__ISNATKIND(1 + z035) :|: z035 >= 0, z = 1 + (1 + z035) A__ISNAT(z) -{ 1 }-> 1 + A__U21(2, 0) + A__ISNATKIND(0) :|: z = 1 + 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1 + z0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z033), 1 + z113), 1 + z033 + z113) + A__ISNATILISTKIND(1 + z033 + z113) :|: z = 1 + (1 + z033 + z113), z033 >= 0, z113 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z034), 1 + z114), 1 + z034 + z114) + A__ISNATILISTKIND(1 + z034 + z114) :|: z114 >= 0, z034 >= 0, z = 1 + (1 + z034 + z114) A__ISNAT(z) -{ 1 }-> 1 + A__U11(2, 3) + A__ISNATILISTKIND(3) :|: z = 1 + 3 A__ISNAT(z) -{ 1 }-> 1 + A__U11(2, 1) + A__ISNATILISTKIND(1) :|: z = 1 + 1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(0, z0) + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(1 + z0, z0) + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(a__and(a__isNatKind(z037), 1 + z115), 1 + z037 + z115) + A__ISNATILISTKIND(1 + z037 + z115) :|: z115 >= 0, z = 1 + z037 + z115, z037 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(a__and(a__isNatKind(z038), 1 + z116), 1 + z038 + z116) + A__ISNATILISTKIND(1 + z038 + z116) :|: z = 1 + z038 + z116, z038 >= 0, z116 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(2, 3) + A__ISNATILISTKIND(3) :|: z = 3 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(2, 1) + A__ISNATILISTKIND(1) :|: z = 1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(0, z0) + A__ISNATILISTKIND(z0) :|: z = z0, z0 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(1 + z0, z0) + A__ISNATILISTKIND(z0) :|: z = z0, z0 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z040), 1 + z1), 1 + z040, z1) + A__AND(a__isNatKind(z040), 1 + z1) + A__ISNATKIND(1 + z040) :|: z1 >= 0, z040 >= 0, z = 1 + (1 + z040) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z040), 1 + z1), 1 + z040, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z040) :|: z1 >= 0, z040 >= 0, z = 1 + (1 + z040) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z040), 1 + z1), 1 + z040, z1) + A__AND(1 + (1 + z040), 1 + z1) + A__ISNATKIND(1 + z040) :|: z1 >= 0, z040 >= 0, z = 1 + (1 + z040) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z039), 1 + z1), 1 + z039, z1) + A__AND(a__isNatIListKind(z039), 1 + z1) + A__ISNATKIND(1 + z039) :|: z1 >= 0, z039 >= 0, z = 1 + (1 + z039) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z039), 1 + z1), 1 + z039, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z039) :|: z1 >= 0, z039 >= 0, z = 1 + (1 + z039) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z039), 1 + z1), 1 + z039, z1) + A__AND(1 + (1 + z039), 1 + z1) + A__ISNATKIND(1 + z039) :|: z1 >= 0, z039 >= 0, z = 1 + (1 + z039) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + z1), 0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + z1), 0, z1) + A__AND(1 + 0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 1 + z043, z1) + A__AND(a__isNatIListKind(z043), 1 + z1) + A__ISNATKIND(1 + z043) :|: z1 >= 0, z043 >= 0, z = 1 + (1 + z043) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 1 + z044, z1) + A__AND(a__isNatKind(z044), 1 + z1) + A__ISNATKIND(1 + z044) :|: z1 >= 0, z044 >= 0, z = 1 + (1 + z044) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + 0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + (1 + z041), 1 + z1), 1 + z041, z1) + A__AND(a__isNatIListKind(z041), 1 + z1) + A__ISNATKIND(1 + z041) :|: z1 >= 0, z041 >= 0, z = 1 + (1 + z041) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + (1 + z042), 1 + z1), 1 + z042, z1) + A__AND(a__isNatKind(z042), 1 + z1) + A__ISNATKIND(1 + z042) :|: z042 >= 0, z1 >= 0, z = 1 + (1 + z042) + z1 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z046), 1 + z1) + A__ISNATKIND(1 + z046) :|: z = 1 + (1 + z046) + z1, z046 >= 0, z1 >= 0 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z048), 1 + z1) + A__ISNATKIND(1 + z048) :|: z1 >= 0, z = 1 + (1 + z048) + z1, z048 >= 0 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatIListKind(z045), 1 + z1) + A__ISNATKIND(1 + z045) :|: z1 >= 0, z045 >= 0, z = 1 + (1 + z045) + z1 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatIListKind(z047), 1 + z1) + A__ISNATKIND(1 + z047) :|: z1 >= 0, z = 1 + (1 + z047) + z1, z047 >= 0 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatKind(z056), 1 + z1), 1 + z056, z1) + A__AND(a__isNatKind(z056), 1 + z1) + A__ISNATKIND(1 + z056) :|: z056 >= 0, z1 >= 0, z = 1 + (1 + z056) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatKind(z056), 1 + z1), 1 + z056, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z056) :|: z056 >= 0, z1 >= 0, z = 1 + (1 + z056) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatKind(z056), 1 + z1), 1 + z056, z1) + A__AND(1 + (1 + z056), 1 + z1) + A__ISNATKIND(1 + z056) :|: z056 >= 0, z1 >= 0, z = 1 + (1 + z056) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatIListKind(z055), 1 + z1), 1 + z055, z1) + A__AND(a__isNatIListKind(z055), 1 + z1) + A__ISNATKIND(1 + z055) :|: z1 >= 0, z055 >= 0, z = 1 + (1 + z055) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatIListKind(z055), 1 + z1), 1 + z055, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z055) :|: z1 >= 0, z055 >= 0, z = 1 + (1 + z055) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatIListKind(z055), 1 + z1), 1 + z055, z1) + A__AND(1 + (1 + z055), 1 + z1) + A__ISNATKIND(1 + z055) :|: z1 >= 0, z055 >= 0, z = 1 + (1 + z055) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(2, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(2, 1 + z1), 0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(2, 1 + z1), 0, z1) + A__AND(1 + 0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + z1), 1 + z059, z1) + A__AND(a__isNatIListKind(z059), 1 + z1) + A__ISNATKIND(1 + z059) :|: z = 1 + (1 + z059) + z1, z1 >= 0, z059 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + z1), 1 + z060, z1) + A__AND(a__isNatKind(z060), 1 + z1) + A__ISNATKIND(1 + z060) :|: z1 >= 0, z = 1 + (1 + z060) + z1, z060 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + 0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + (1 + z057), 1 + z1), 1 + z057, z1) + A__AND(a__isNatIListKind(z057), 1 + z1) + A__ISNATKIND(1 + z057) :|: z1 >= 0, z = 1 + (1 + z057) + z1, z057 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + (1 + z058), 1 + z1), 1 + z058, z1) + A__AND(a__isNatKind(z058), 1 + z1) + A__ISNATKIND(1 + z058) :|: z1 >= 0, z058 >= 0, z = 1 + (1 + z058) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z050), 1 + z1), 1 + z050, z1) + A__AND(a__isNatKind(z050), 1 + z1) + A__ISNATKIND(1 + z050) :|: z1 >= 0, z = 1 + (1 + z050) + z1, z050 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z050), 1 + z1), 1 + z050, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z050) :|: z1 >= 0, z = 1 + (1 + z050) + z1, z050 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z050), 1 + z1), 1 + z050, z1) + A__AND(1 + (1 + z050), 1 + z1) + A__ISNATKIND(1 + z050) :|: z1 >= 0, z = 1 + (1 + z050) + z1, z050 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z049), 1 + z1), 1 + z049, z1) + A__AND(a__isNatIListKind(z049), 1 + z1) + A__ISNATKIND(1 + z049) :|: z1 >= 0, z049 >= 0, z = 1 + (1 + z049) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z049), 1 + z1), 1 + z049, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z049) :|: z1 >= 0, z049 >= 0, z = 1 + (1 + z049) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z049), 1 + z1), 1 + z049, z1) + A__AND(1 + (1 + z049), 1 + z1) + A__ISNATKIND(1 + z049) :|: z1 >= 0, z049 >= 0, z = 1 + (1 + z049) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + z1), 0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + z1), 0, z1) + A__AND(1 + 0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 1 + z053, z1) + A__AND(a__isNatIListKind(z053), 1 + z1) + A__ISNATKIND(1 + z053) :|: z1 >= 0, z053 >= 0, z = 1 + (1 + z053) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 1 + z054, z1) + A__AND(a__isNatKind(z054), 1 + z1) + A__ISNATKIND(1 + z054) :|: z = 1 + (1 + z054) + z1, z1 >= 0, z054 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + 0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + (1 + z051), 1 + z1), 1 + z051, z1) + A__AND(a__isNatIListKind(z051), 1 + z1) + A__ISNATKIND(1 + z051) :|: z1 >= 0, z = 1 + (1 + z051) + z1, z051 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + (1 + z052), 1 + z1), 1 + z052, z1) + A__AND(a__isNatKind(z052), 1 + z1) + A__ISNATKIND(1 + z052) :|: z = 1 + (1 + z052) + z1, z052 >= 0, z1 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__U71(a__and(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) + A__AND(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)) + A__AND(a__isNatList(z1), 1 + z1) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(a__U41(a__and(a__isNatKind(z02356), 1 + z11178), z02356, z11178), 1 + (1 + z02356 + z11178)) + A__ISNATILIST(1 + z02356 + z11178) :|: z' = 1 + z02356 + z11178, z11178 >= 0, z = 0, z02356 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(a__U31(a__isNatIListKind(z0), z0), 1 + z0) + A__ISNATILIST(z0) :|: z0 >= 0, z = 0, z' = z0 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(2, 1 + 3) + A__ISNATILIST(3) :|: z' = 3, z = 0 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(0, 1 + z0) + A__ISNATILIST(z0) :|: z0 >= 0, z = 0, z' = z0 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(1 + z0, 1 + z0) + A__ISNATILIST(z0) :|: z0 >= 0, z = 0, z' = z0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(a__and(a__and(a__isNatIList(z2), 1 + z2), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))), z2, z0, z1) + A__AND(a__and(a__isNatIList(z2), 1 + z2), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))) + A__AND(a__isNatIList(z2), 1 + z2) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__U11(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U21(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 2, z0 >= 0, z' = z0 A__U31(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U21(a__isNatKind(z0''), z0''), z1) + A__ISNAT(1 + z0'') :|: z = 2, z1 >= 0, z' = 1 + z0'', z0'' >= 0, z'' = z1 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U11(a__isNatIListKind(z0'), z0'), z1) + A__ISNAT(1 + z0') :|: z = 2, z1 >= 0, z0' >= 0, z' = 1 + z0', z'' = z1 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(2, z1) + A__ISNAT(0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(1 + z0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U42(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__U21(a__isNatKind(z02), z02), z1) + A__ISNAT(1 + z02) :|: z = 2, z1 >= 0, z02 >= 0, z' = 1 + z02, z'' = z1 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__U11(a__isNatIListKind(z01), z01), z1) + A__ISNAT(1 + z01) :|: z = 2, z1 >= 0, z01 >= 0, z' = 1 + z01, z'' = z1 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(2, z1) + A__ISNAT(0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(1 + z0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U52(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(a__U21(a__isNatKind(z04), z04), z1) + A__ISNAT(1 + z04) :|: z = 2, z04 >= 0, z1 >= 0, z' = 1 + z04, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(a__U11(a__isNatIListKind(z03), z03), z1) + A__ISNAT(1 + z03) :|: z = 2, z1 >= 0, z' = 1 + z03, z03 >= 0, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(2, z1) + A__ISNAT(0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(1 + z0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U62(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U71(z, z') -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__U91(z, z', z'', z4) -{ 1 }-> 1 + MARK(z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U91(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U71(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U62(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U52(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U42(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__U11(z, z') -{ 0 }-> a__U12(a__U61(a__and(a__isNatKind(z02358), 1 + z11180), z02358, z11180)) :|: z = 2, z11180 >= 0, z' = 1 + z02358 + z11180, z02358 >= 0 a__U11(z, z') -{ 0 }-> a__U12(a__U51(a__and(a__isNatKind(z02357), 1 + z11179), z02357, z11179)) :|: z = 2, z' = 1 + z02357 + z11179, z11179 >= 0, z02357 >= 0 a__U11(z, z') -{ 0 }-> a__U12(2) :|: z = 2, z' = 1 a__U11(z, z') -{ 0 }-> a__U12(0) :|: z = 2, z0 >= 0, z' = z0 a__U11(z, z') -{ 0 }-> a__U12(1 + z0) :|: z = 2, z0 >= 0, z' = z0 a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U12(z) -{ 0 }-> 2 :|: z = 2 a__U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U12(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U21(a__isNatKind(z02360), z02360)) :|: z = 2, z' = 1 + z02360, z02360 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U11(a__isNatIListKind(z02359), z02359)) :|: z = 2, z02359 >= 0, z' = 1 + z02359 a__U21(z, z') -{ 0 }-> a__U22(2) :|: z = 2, z' = 0 a__U21(z, z') -{ 0 }-> a__U22(0) :|: z = 2, z0 >= 0, z' = z0 a__U21(z, z') -{ 0 }-> a__U22(1 + z0) :|: z = 2, z0 >= 0, z' = z0 a__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U21(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U22(z) -{ 0 }-> 2 :|: z = 2 a__U22(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U22(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U31(z, z') -{ 0 }-> a__U32(a__U61(a__and(a__isNatKind(z02362), 1 + z11182), z02362, z11182)) :|: z = 2, z02362 >= 0, z' = 1 + z02362 + z11182, z11182 >= 0 a__U31(z, z') -{ 0 }-> a__U32(a__U51(a__and(a__isNatKind(z02361), 1 + z11181), z02361, z11181)) :|: z = 2, z11181 >= 0, z02361 >= 0, z' = 1 + z02361 + z11181 a__U31(z, z') -{ 0 }-> a__U32(2) :|: z = 2, z' = 1 a__U31(z, z') -{ 0 }-> a__U32(0) :|: z = 2, z0 >= 0, z' = z0 a__U31(z, z') -{ 0 }-> a__U32(1 + z0) :|: z = 2, z0 >= 0, z' = z0 a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U32(z) -{ 0 }-> 2 :|: z = 2 a__U32(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U32(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U41(z, z', z'') -{ 0 }-> a__U42(a__U21(a__isNatKind(z02364), z02364), z1) :|: z = 2, z1 >= 0, z02364 >= 0, z' = 1 + z02364, z'' = z1 a__U41(z, z', z'') -{ 0 }-> a__U42(a__U11(a__isNatIListKind(z02363), z02363), z1) :|: z = 2, z1 >= 0, z02363 >= 0, z' = 1 + z02363, z'' = z1 a__U41(z, z', z'') -{ 0 }-> a__U42(2, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1 a__U41(z, z', z'') -{ 0 }-> a__U42(0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U41(z, z', z'') -{ 0 }-> a__U42(1 + z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U41(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U42(z, z') -{ 0 }-> a__U43(a__U41(a__and(a__isNatKind(z02365), 1 + z11183), z02365, z11183)) :|: z = 2, z11183 >= 0, z02365 >= 0, z' = 1 + z02365 + z11183 a__U42(z, z') -{ 0 }-> a__U43(a__U31(a__isNatIListKind(z0), z0)) :|: z = 2, z0 >= 0, z' = z0 a__U42(z, z') -{ 0 }-> a__U43(2) :|: z = 2, z' = 3 a__U42(z, z') -{ 0 }-> a__U43(0) :|: z = 2, z0 >= 0, z' = z0 a__U42(z, z') -{ 0 }-> a__U43(1 + z0) :|: z = 2, z0 >= 0, z' = z0 a__U42(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U42(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U43(z) -{ 0 }-> 2 :|: z = 2 a__U43(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U43(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U51(z, z', z'') -{ 0 }-> a__U52(a__U21(a__isNatKind(z02367), z02367), z1) :|: z = 2, z1 >= 0, z' = 1 + z02367, z02367 >= 0, z'' = z1 a__U51(z, z', z'') -{ 0 }-> a__U52(a__U11(a__isNatIListKind(z02366), z02366), z1) :|: z = 2, z02366 >= 0, z1 >= 0, z' = 1 + z02366, z'' = z1 a__U51(z, z', z'') -{ 0 }-> a__U52(2, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1 a__U51(z, z', z'') -{ 0 }-> a__U52(0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U51(z, z', z'') -{ 0 }-> a__U52(1 + z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U51(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U51(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U52(z, z') -{ 0 }-> a__U53(a__U61(a__and(a__isNatKind(z02369), 1 + z11185), z02369, z11185)) :|: z = 2, z11185 >= 0, z02369 >= 0, z' = 1 + z02369 + z11185 a__U52(z, z') -{ 0 }-> a__U53(a__U51(a__and(a__isNatKind(z02368), 1 + z11184), z02368, z11184)) :|: z = 2, z' = 1 + z02368 + z11184, z11184 >= 0, z02368 >= 0 a__U52(z, z') -{ 0 }-> a__U53(2) :|: z = 2, z' = 1 a__U52(z, z') -{ 0 }-> a__U53(0) :|: z = 2, z0 >= 0, z' = z0 a__U52(z, z') -{ 0 }-> a__U53(1 + z0) :|: z = 2, z0 >= 0, z' = z0 a__U52(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U52(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U53(z) -{ 0 }-> 2 :|: z = 2 a__U53(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U53(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U61(z, z', z'') -{ 0 }-> a__U62(a__U21(a__isNatKind(z02371), z02371), z1) :|: z = 2, z1 >= 0, z02371 >= 0, z' = 1 + z02371, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(a__U11(a__isNatIListKind(z02370), z02370), z1) :|: z = 2, z1 >= 0, z02370 >= 0, z' = 1 + z02370, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(2, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(1 + z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U61(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U62(z, z') -{ 0 }-> a__U63(a__U41(a__and(a__isNatKind(z02372), 1 + z11186), z02372, z11186)) :|: z = 2, z02372 >= 0, z11186 >= 0, z' = 1 + z02372 + z11186 a__U62(z, z') -{ 0 }-> a__U63(a__U31(a__isNatIListKind(z0), z0)) :|: z = 2, z0 >= 0, z' = z0 a__U62(z, z') -{ 0 }-> a__U63(2) :|: z = 2, z' = 3 a__U62(z, z') -{ 0 }-> a__U63(0) :|: z = 2, z0 >= 0, z' = z0 a__U62(z, z') -{ 0 }-> a__U63(1 + z0) :|: z = 2, z0 >= 0, z' = z0 a__U62(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U62(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U63(z) -{ 0 }-> 2 :|: z = 2 a__U63(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U63(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U71(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U71(z, z') -{ 0 }-> 1 + a__length(mark(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U71(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U81(z) -{ 0 }-> 1 :|: z = 2 a__U81(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U81(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> 1 + mark(z2) + (1 + z1 + z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U91(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__and(z, z') -{ 0 }-> mark(z0) :|: z = 2, z0 >= 0, z' = z0 a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__isNatKind(z02404), 1 + z02404) :|: z02404 >= 0, z = 1 + (1 + z02404) a__isNat(z) -{ 0 }-> a__U21(a__isNatIListKind(z02403), 1 + z02403) :|: z02403 >= 0, z = 1 + (1 + z02403) a__isNat(z) -{ 0 }-> a__U21(2, 0) :|: z = 1 + 0 a__isNat(z) -{ 0 }-> a__U21(0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U21(1 + z0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__and(a__isNatKind(z02401), 1 + z11201), 1 + z02401 + z11201) :|: z = 1 + (1 + z02401 + z11201), z02401 >= 0, z11201 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__and(a__isNatKind(z02402), 1 + z11202), 1 + z02402 + z11202) :|: z02402 >= 0, z11202 >= 0, z = 1 + (1 + z02402 + z11202) a__isNat(z) -{ 0 }-> a__U11(2, 3) :|: z = 1 + 3 a__isNat(z) -{ 0 }-> a__U11(2, 1) :|: z = 1 + 1 a__isNat(z) -{ 0 }-> a__U11(0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(1 + z0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> 2 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> a__U41(a__and(a__isNatKind(z02408), 1 + z1), 1 + z02408, z1) :|: z1 >= 0, z02408 >= 0, z = 1 + (1 + z02408) + z1 a__isNatIList(z) -{ 0 }-> a__U41(a__and(a__isNatIListKind(z02407), 1 + z1), 1 + z02407, z1) :|: z = 1 + (1 + z02407) + z1, z1 >= 0, z02407 >= 0 a__isNatIList(z) -{ 0 }-> a__U41(a__and(2, 1 + z1), 0, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatIList(z) -{ 0 }-> a__U41(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIList(z) -{ 0 }-> a__U41(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIList(z) -{ 0 }-> a__U31(a__and(a__isNatKind(z02405), 1 + z11203), 1 + z02405 + z11203) :|: z02405 >= 0, z11203 >= 0, z = 1 + z02405 + z11203 a__isNatIList(z) -{ 0 }-> a__U31(a__and(a__isNatKind(z02406), 1 + z11204), 1 + z02406 + z11204) :|: z02406 >= 0, z11204 >= 0, z = 1 + z02406 + z11204 a__isNatIList(z) -{ 0 }-> a__U31(2, 3) :|: z = 3 a__isNatIList(z) -{ 0 }-> a__U31(2, 1) :|: z = 1 a__isNatIList(z) -{ 0 }-> a__U31(0, z0) :|: z = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> a__U31(1 + z0, z0) :|: z = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> 2 :|: z = 3 a__isNatIList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatIList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatKind(z02410), 1 + z1) :|: z1 >= 0, z = 1 + (1 + z02410) + z1, z02410 >= 0 a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatKind(z02412), 1 + z1) :|: z1 >= 0, z02412 >= 0, z = 1 + (1 + z02412) + z1 a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatIListKind(z02409), 1 + z1) :|: z = 1 + (1 + z02409) + z1, z1 >= 0, z02409 >= 0 a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatIListKind(z02411), 1 + z1) :|: z = 1 + (1 + z02411) + z1, z1 >= 0, z02411 >= 0 a__isNatIListKind(z) -{ 0 }-> a__and(2, 1 + z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatIListKind(z) -{ 0 }-> a__and(0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIListKind(z) -{ 0 }-> a__and(1 + z0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 1 a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 3 a__isNatIListKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatIListKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__isNatIListKind(z0) :|: z = 1 + z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> 2 :|: z = 0 a__isNatKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__and(a__isNatKind(z02416), 1 + z1), 1 + z02416, z1) :|: z1 >= 0, z = 1 + (1 + z02416) + z1, z02416 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__and(a__isNatIListKind(z02415), 1 + z1), 1 + z02415, z1) :|: z1 >= 0, z = 1 + (1 + z02415) + z1, z02415 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__and(2, 1 + z1), 0, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatList(z) -{ 0 }-> a__U61(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U61(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U51(a__and(a__isNatKind(z02414), 1 + z1), 1 + z02414, z1) :|: z1 >= 0, z = 1 + (1 + z02414) + z1, z02414 >= 0 a__isNatList(z) -{ 0 }-> a__U51(a__and(a__isNatIListKind(z02413), 1 + z1), 1 + z02413, z1) :|: z = 1 + (1 + z02413) + z1, z02413 >= 0, z1 >= 0 a__isNatList(z) -{ 0 }-> a__U51(a__and(2, 1 + z1), 0, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatList(z) -{ 0 }-> a__U51(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U51(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> 2 :|: z = 1 a__isNatList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__length(z) -{ 0 }-> a__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z02418), 1 + z11206), z02418, z11206), 1 + (1 + z02418 + z11206)), 1 + (1 + z0) + (1 + z0)), 1 + z02418 + z11206) :|: z02418 >= 0, z11206 >= 0, z0 >= 0, z = 1 + z0 + (1 + z02418 + z11206) a__length(z) -{ 0 }-> a__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z02417), 1 + z11205), z02417, z11205), 1 + (1 + z02417 + z11205)), 1 + (1 + z0) + (1 + z0)), 1 + z02417 + z11205) :|: z02417 >= 0, z11205 >= 0, z0 >= 0, z = 1 + z0 + (1 + z02417 + z11205) a__length(z) -{ 0 }-> a__U71(a__and(a__and(2, 1 + 1), 1 + (1 + z0) + (1 + z0)), 1) :|: z0 >= 0, z = 1 + z0 + 1 a__length(z) -{ 0 }-> a__U71(a__and(a__and(0, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> a__U71(a__and(a__and(1 + z1, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> 0 :|: z = 1 a__length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__length(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z02420), 1 + z11208), z02420, z11208), 1 + (1 + z02420 + z11208)), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))), 1 + z02420 + z11208, z0, z1) :|: z11208 >= 0, z1 >= 0, z' = 1 + z1 + (1 + z02420 + z11208), z02420 >= 0, z = 1 + z0, z0 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(a__U31(a__isNatIListKind(z2), z2), 1 + z2), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))), z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(2, 1 + 3), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))), 3, z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1 + 3 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(0, 1 + z2), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))), z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(1 + z2, 1 + z2), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))), z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U81(a__and(a__U41(a__and(a__isNatKind(z02419), 1 + z11207), z02419, z11207), 1 + (1 + z02419 + z11207))) :|: z11207 >= 0, z02419 >= 0, z' = 1 + z02419 + z11207, z = 0 a__take(z, z') -{ 0 }-> a__U81(a__and(a__U31(a__isNatIListKind(z0), z0), 1 + z0)) :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> a__U81(a__and(2, 1 + 3)) :|: z' = 3, z = 0 a__take(z, z') -{ 0 }-> a__U81(a__and(0, 1 + z0)) :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> a__U81(a__and(1 + z0, 1 + z0)) :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__take(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: mark(z) -{ 0 }-> a__zeros :|: z = 3 mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__length(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatList(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatIListKind(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatIList(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__and(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U91(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U81(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U71(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U63(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U62(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U61(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U53(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U52(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U51(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U43(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U42(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U41(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U32(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U22(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U21(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U12(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U11(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ---------------------------------------- (55) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: a__U12(z) -{ 0 }-> 2 :|: z = 2 a__U12(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U22(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U22(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U22(z) -{ 0 }-> 2 :|: z = 2 a__U32(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U32(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U32(z) -{ 0 }-> 2 :|: z = 2 a__U43(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U43(z) -{ 0 }-> 2 :|: z = 2 a__U43(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U53(z) -{ 0 }-> 2 :|: z = 2 a__U53(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U53(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U63(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U63(z) -{ 0 }-> 2 :|: z = 2 a__U63(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U81(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U81(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U81(z) -{ 0 }-> 1 :|: z = 2 ---------------------------------------- (56) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z036), 1 + z036) + A__ISNATKIND(1 + z036) :|: z036 >= 0, z = 1 + (1 + z036) A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatIListKind(z035), 1 + z035) + A__ISNATKIND(1 + z035) :|: z035 >= 0, z = 1 + (1 + z035) A__ISNAT(z) -{ 1 }-> 1 + A__U21(2, 0) + A__ISNATKIND(0) :|: z = 1 + 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1 + z0, z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z033), 1 + z113), 1 + z033 + z113) + A__ISNATILISTKIND(1 + z033 + z113) :|: z = 1 + (1 + z033 + z113), z033 >= 0, z113 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z034), 1 + z114), 1 + z034 + z114) + A__ISNATILISTKIND(1 + z034 + z114) :|: z114 >= 0, z034 >= 0, z = 1 + (1 + z034 + z114) A__ISNAT(z) -{ 1 }-> 1 + A__U11(2, 3) + A__ISNATILISTKIND(3) :|: z = 1 + 3 A__ISNAT(z) -{ 1 }-> 1 + A__U11(2, 1) + A__ISNATILISTKIND(1) :|: z = 1 + 1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(0, z0) + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(1 + z0, z0) + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(a__and(a__isNatKind(z037), 1 + z115), 1 + z037 + z115) + A__ISNATILISTKIND(1 + z037 + z115) :|: z115 >= 0, z = 1 + z037 + z115, z037 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(a__and(a__isNatKind(z038), 1 + z116), 1 + z038 + z116) + A__ISNATILISTKIND(1 + z038 + z116) :|: z = 1 + z038 + z116, z038 >= 0, z116 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(2, 3) + A__ISNATILISTKIND(3) :|: z = 3 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(2, 1) + A__ISNATILISTKIND(1) :|: z = 1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(0, z0) + A__ISNATILISTKIND(z0) :|: z = z0, z0 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(1 + z0, z0) + A__ISNATILISTKIND(z0) :|: z = z0, z0 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z040), 1 + z1), 1 + z040, z1) + A__AND(a__isNatKind(z040), 1 + z1) + A__ISNATKIND(1 + z040) :|: z1 >= 0, z040 >= 0, z = 1 + (1 + z040) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z040), 1 + z1), 1 + z040, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z040) :|: z1 >= 0, z040 >= 0, z = 1 + (1 + z040) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z040), 1 + z1), 1 + z040, z1) + A__AND(1 + (1 + z040), 1 + z1) + A__ISNATKIND(1 + z040) :|: z1 >= 0, z040 >= 0, z = 1 + (1 + z040) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z039), 1 + z1), 1 + z039, z1) + A__AND(a__isNatIListKind(z039), 1 + z1) + A__ISNATKIND(1 + z039) :|: z1 >= 0, z039 >= 0, z = 1 + (1 + z039) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z039), 1 + z1), 1 + z039, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z039) :|: z1 >= 0, z039 >= 0, z = 1 + (1 + z039) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z039), 1 + z1), 1 + z039, z1) + A__AND(1 + (1 + z039), 1 + z1) + A__ISNATKIND(1 + z039) :|: z1 >= 0, z039 >= 0, z = 1 + (1 + z039) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + z1), 0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + z1), 0, z1) + A__AND(1 + 0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 1 + z043, z1) + A__AND(a__isNatIListKind(z043), 1 + z1) + A__ISNATKIND(1 + z043) :|: z1 >= 0, z043 >= 0, z = 1 + (1 + z043) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 1 + z044, z1) + A__AND(a__isNatKind(z044), 1 + z1) + A__ISNATKIND(1 + z044) :|: z1 >= 0, z044 >= 0, z = 1 + (1 + z044) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + 0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + (1 + z041), 1 + z1), 1 + z041, z1) + A__AND(a__isNatIListKind(z041), 1 + z1) + A__ISNATKIND(1 + z041) :|: z1 >= 0, z041 >= 0, z = 1 + (1 + z041) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + (1 + z042), 1 + z1), 1 + z042, z1) + A__AND(a__isNatKind(z042), 1 + z1) + A__ISNATKIND(1 + z042) :|: z042 >= 0, z1 >= 0, z = 1 + (1 + z042) + z1 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z046), 1 + z1) + A__ISNATKIND(1 + z046) :|: z = 1 + (1 + z046) + z1, z046 >= 0, z1 >= 0 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z048), 1 + z1) + A__ISNATKIND(1 + z048) :|: z1 >= 0, z = 1 + (1 + z048) + z1, z048 >= 0 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatIListKind(z045), 1 + z1) + A__ISNATKIND(1 + z045) :|: z1 >= 0, z045 >= 0, z = 1 + (1 + z045) + z1 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatIListKind(z047), 1 + z1) + A__ISNATKIND(1 + z047) :|: z1 >= 0, z = 1 + (1 + z047) + z1, z047 >= 0 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatKind(z056), 1 + z1), 1 + z056, z1) + A__AND(a__isNatKind(z056), 1 + z1) + A__ISNATKIND(1 + z056) :|: z056 >= 0, z1 >= 0, z = 1 + (1 + z056) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatKind(z056), 1 + z1), 1 + z056, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z056) :|: z056 >= 0, z1 >= 0, z = 1 + (1 + z056) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatKind(z056), 1 + z1), 1 + z056, z1) + A__AND(1 + (1 + z056), 1 + z1) + A__ISNATKIND(1 + z056) :|: z056 >= 0, z1 >= 0, z = 1 + (1 + z056) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatIListKind(z055), 1 + z1), 1 + z055, z1) + A__AND(a__isNatIListKind(z055), 1 + z1) + A__ISNATKIND(1 + z055) :|: z1 >= 0, z055 >= 0, z = 1 + (1 + z055) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatIListKind(z055), 1 + z1), 1 + z055, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z055) :|: z1 >= 0, z055 >= 0, z = 1 + (1 + z055) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatIListKind(z055), 1 + z1), 1 + z055, z1) + A__AND(1 + (1 + z055), 1 + z1) + A__ISNATKIND(1 + z055) :|: z1 >= 0, z055 >= 0, z = 1 + (1 + z055) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(2, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(2, 1 + z1), 0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(2, 1 + z1), 0, z1) + A__AND(1 + 0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + z1), 1 + z059, z1) + A__AND(a__isNatIListKind(z059), 1 + z1) + A__ISNATKIND(1 + z059) :|: z = 1 + (1 + z059) + z1, z1 >= 0, z059 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + z1), 1 + z060, z1) + A__AND(a__isNatKind(z060), 1 + z1) + A__ISNATKIND(1 + z060) :|: z1 >= 0, z = 1 + (1 + z060) + z1, z060 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + 0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + (1 + z057), 1 + z1), 1 + z057, z1) + A__AND(a__isNatIListKind(z057), 1 + z1) + A__ISNATKIND(1 + z057) :|: z1 >= 0, z = 1 + (1 + z057) + z1, z057 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + (1 + z058), 1 + z1), 1 + z058, z1) + A__AND(a__isNatKind(z058), 1 + z1) + A__ISNATKIND(1 + z058) :|: z1 >= 0, z058 >= 0, z = 1 + (1 + z058) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z050), 1 + z1), 1 + z050, z1) + A__AND(a__isNatKind(z050), 1 + z1) + A__ISNATKIND(1 + z050) :|: z1 >= 0, z = 1 + (1 + z050) + z1, z050 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z050), 1 + z1), 1 + z050, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z050) :|: z1 >= 0, z = 1 + (1 + z050) + z1, z050 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z050), 1 + z1), 1 + z050, z1) + A__AND(1 + (1 + z050), 1 + z1) + A__ISNATKIND(1 + z050) :|: z1 >= 0, z = 1 + (1 + z050) + z1, z050 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z049), 1 + z1), 1 + z049, z1) + A__AND(a__isNatIListKind(z049), 1 + z1) + A__ISNATKIND(1 + z049) :|: z1 >= 0, z049 >= 0, z = 1 + (1 + z049) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z049), 1 + z1), 1 + z049, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z049) :|: z1 >= 0, z049 >= 0, z = 1 + (1 + z049) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z049), 1 + z1), 1 + z049, z1) + A__AND(1 + (1 + z049), 1 + z1) + A__ISNATKIND(1 + z049) :|: z1 >= 0, z049 >= 0, z = 1 + (1 + z049) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + z1), 0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + z1), 0, z1) + A__AND(1 + 0, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 1 + z053, z1) + A__AND(a__isNatIListKind(z053), 1 + z1) + A__ISNATKIND(1 + z053) :|: z1 >= 0, z053 >= 0, z = 1 + (1 + z053) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 1 + z054, z1) + A__AND(a__isNatKind(z054), 1 + z1) + A__ISNATKIND(1 + z054) :|: z = 1 + (1 + z054) + z1, z1 >= 0, z054 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + 0, 1 + z1), 0, z1) + A__AND(2, 1 + z1) + A__ISNATKIND(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + (1 + z051), 1 + z1), 1 + z051, z1) + A__AND(a__isNatIListKind(z051), 1 + z1) + A__ISNATKIND(1 + z051) :|: z1 >= 0, z = 1 + (1 + z051) + z1, z051 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + (1 + z052), 1 + z1), 1 + z052, z1) + A__AND(a__isNatKind(z052), 1 + z1) + A__ISNATKIND(1 + z052) :|: z = 1 + (1 + z052) + z1, z052 >= 0, z1 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__U71(a__and(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) + A__AND(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)) + A__AND(a__isNatList(z1), 1 + z1) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(a__U41(a__and(a__isNatKind(z02356), 1 + z11178), z02356, z11178), 1 + (1 + z02356 + z11178)) + A__ISNATILIST(1 + z02356 + z11178) :|: z' = 1 + z02356 + z11178, z11178 >= 0, z = 0, z02356 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(a__U31(a__isNatIListKind(z0), z0), 1 + z0) + A__ISNATILIST(z0) :|: z0 >= 0, z = 0, z' = z0 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(2, 1 + 3) + A__ISNATILIST(3) :|: z' = 3, z = 0 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(0, 1 + z0) + A__ISNATILIST(z0) :|: z0 >= 0, z = 0, z' = z0 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(1 + z0, 1 + z0) + A__ISNATILIST(z0) :|: z0 >= 0, z = 0, z' = z0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(a__and(a__and(a__isNatIList(z2), 1 + z2), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))), z2, z0, z1) + A__AND(a__and(a__isNatIList(z2), 1 + z2), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))) + A__AND(a__isNatIList(z2), 1 + z2) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__U11(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U21(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 2, z0 >= 0, z' = z0 A__U31(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U21(a__isNatKind(z0''), z0''), z1) + A__ISNAT(1 + z0'') :|: z = 2, z1 >= 0, z' = 1 + z0'', z0'' >= 0, z'' = z1 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U11(a__isNatIListKind(z0'), z0'), z1) + A__ISNAT(1 + z0') :|: z = 2, z1 >= 0, z0' >= 0, z' = 1 + z0', z'' = z1 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(2, z1) + A__ISNAT(0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(1 + z0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U42(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__U21(a__isNatKind(z02), z02), z1) + A__ISNAT(1 + z02) :|: z = 2, z1 >= 0, z02 >= 0, z' = 1 + z02, z'' = z1 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__U11(a__isNatIListKind(z01), z01), z1) + A__ISNAT(1 + z01) :|: z = 2, z1 >= 0, z01 >= 0, z' = 1 + z01, z'' = z1 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(2, z1) + A__ISNAT(0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(1 + z0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U52(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(a__U21(a__isNatKind(z04), z04), z1) + A__ISNAT(1 + z04) :|: z = 2, z04 >= 0, z1 >= 0, z' = 1 + z04, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(a__U11(a__isNatIListKind(z03), z03), z1) + A__ISNAT(1 + z03) :|: z = 2, z1 >= 0, z' = 1 + z03, z03 >= 0, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(2, z1) + A__ISNAT(0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(1 + z0, z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U62(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U71(z, z') -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__U91(z, z', z'', z4) -{ 1 }-> 1 + MARK(z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U91(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U71(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U62(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U52(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U42(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__U11(z, z') -{ 0 }-> a__U12(a__U61(a__and(a__isNatKind(z02358), 1 + z11180), z02358, z11180)) :|: z = 2, z11180 >= 0, z' = 1 + z02358 + z11180, z02358 >= 0 a__U11(z, z') -{ 0 }-> a__U12(a__U51(a__and(a__isNatKind(z02357), 1 + z11179), z02357, z11179)) :|: z = 2, z' = 1 + z02357 + z11179, z11179 >= 0, z02357 >= 0 a__U11(z, z') -{ 0 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U11(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = 2 a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U11(z, z') -{ 0 }-> 0 :|: z = 2, z' = 1, v0 >= 0, 2 = v0 a__U11(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__U11(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 0 = v0 a__U11(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 1, 2 = z0, z0 >= 0 a__U11(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__U11(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 0 = z0', z0' >= 0 a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U12(z) -{ 0 }-> 2 :|: z = 2 a__U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U12(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U21(a__isNatKind(z02360), z02360)) :|: z = 2, z' = 1 + z02360, z02360 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U11(a__isNatIListKind(z02359), z02359)) :|: z = 2, z02359 >= 0, z' = 1 + z02359 a__U21(z, z') -{ 0 }-> 2 :|: z = 2, z' = 0, 2 = 2 a__U21(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = 2 a__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U21(z, z') -{ 0 }-> 0 :|: z = 2, z' = 0, v0 >= 0, 2 = v0 a__U21(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__U21(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 0 = v0 a__U21(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 0, 2 = z0, z0 >= 0 a__U21(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__U21(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 0 = z0', z0' >= 0 a__U21(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U22(z) -{ 0 }-> 2 :|: z = 2 a__U22(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U22(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U31(z, z') -{ 0 }-> a__U32(a__U61(a__and(a__isNatKind(z02362), 1 + z11182), z02362, z11182)) :|: z = 2, z02362 >= 0, z' = 1 + z02362 + z11182, z11182 >= 0 a__U31(z, z') -{ 0 }-> a__U32(a__U51(a__and(a__isNatKind(z02361), 1 + z11181), z02361, z11181)) :|: z = 2, z11181 >= 0, z02361 >= 0, z' = 1 + z02361 + z11181 a__U31(z, z') -{ 0 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U31(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = 2 a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U31(z, z') -{ 0 }-> 0 :|: z = 2, z' = 1, v0 >= 0, 2 = v0 a__U31(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__U31(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 0 = v0 a__U31(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 1, 2 = z0, z0 >= 0 a__U31(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__U31(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 0 = z0', z0' >= 0 a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U32(z) -{ 0 }-> 2 :|: z = 2 a__U32(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U32(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U41(z, z', z'') -{ 0 }-> a__U42(a__U21(a__isNatKind(z02364), z02364), z1) :|: z = 2, z1 >= 0, z02364 >= 0, z' = 1 + z02364, z'' = z1 a__U41(z, z', z'') -{ 0 }-> a__U42(a__U11(a__isNatIListKind(z02363), z02363), z1) :|: z = 2, z1 >= 0, z02363 >= 0, z' = 1 + z02363, z'' = z1 a__U41(z, z', z'') -{ 0 }-> a__U42(2, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1 a__U41(z, z', z'') -{ 0 }-> a__U42(0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U41(z, z', z'') -{ 0 }-> a__U42(1 + z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U41(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U42(z, z') -{ 0 }-> a__U43(a__U41(a__and(a__isNatKind(z02365), 1 + z11183), z02365, z11183)) :|: z = 2, z11183 >= 0, z02365 >= 0, z' = 1 + z02365 + z11183 a__U42(z, z') -{ 0 }-> a__U43(a__U31(a__isNatIListKind(z0), z0)) :|: z = 2, z0 >= 0, z' = z0 a__U42(z, z') -{ 0 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U42(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = 2 a__U42(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U42(z, z') -{ 0 }-> 0 :|: z = 2, z' = 3, v0 >= 0, 2 = v0 a__U42(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__U42(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 0 = v0 a__U42(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 3, 2 = z0, z0 >= 0 a__U42(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__U42(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 0 = z0', z0' >= 0 a__U42(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U43(z) -{ 0 }-> 2 :|: z = 2 a__U43(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U43(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U51(z, z', z'') -{ 0 }-> a__U52(a__U21(a__isNatKind(z02367), z02367), z1) :|: z = 2, z1 >= 0, z' = 1 + z02367, z02367 >= 0, z'' = z1 a__U51(z, z', z'') -{ 0 }-> a__U52(a__U11(a__isNatIListKind(z02366), z02366), z1) :|: z = 2, z02366 >= 0, z1 >= 0, z' = 1 + z02366, z'' = z1 a__U51(z, z', z'') -{ 0 }-> a__U52(2, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1 a__U51(z, z', z'') -{ 0 }-> a__U52(0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U51(z, z', z'') -{ 0 }-> a__U52(1 + z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U51(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U51(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U52(z, z') -{ 0 }-> a__U53(a__U61(a__and(a__isNatKind(z02369), 1 + z11185), z02369, z11185)) :|: z = 2, z11185 >= 0, z02369 >= 0, z' = 1 + z02369 + z11185 a__U52(z, z') -{ 0 }-> a__U53(a__U51(a__and(a__isNatKind(z02368), 1 + z11184), z02368, z11184)) :|: z = 2, z' = 1 + z02368 + z11184, z11184 >= 0, z02368 >= 0 a__U52(z, z') -{ 0 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U52(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = 2 a__U52(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U52(z, z') -{ 0 }-> 0 :|: z = 2, z' = 1, v0 >= 0, 2 = v0 a__U52(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__U52(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 0 = v0 a__U52(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 1, 2 = z0, z0 >= 0 a__U52(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__U52(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 0 = z0', z0' >= 0 a__U52(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U53(z) -{ 0 }-> 2 :|: z = 2 a__U53(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U53(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U61(z, z', z'') -{ 0 }-> a__U62(a__U21(a__isNatKind(z02371), z02371), z1) :|: z = 2, z1 >= 0, z02371 >= 0, z' = 1 + z02371, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(a__U11(a__isNatIListKind(z02370), z02370), z1) :|: z = 2, z1 >= 0, z02370 >= 0, z' = 1 + z02370, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(2, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> a__U62(1 + z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U61(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U62(z, z') -{ 0 }-> a__U63(a__U41(a__and(a__isNatKind(z02372), 1 + z11186), z02372, z11186)) :|: z = 2, z02372 >= 0, z11186 >= 0, z' = 1 + z02372 + z11186 a__U62(z, z') -{ 0 }-> a__U63(a__U31(a__isNatIListKind(z0), z0)) :|: z = 2, z0 >= 0, z' = z0 a__U62(z, z') -{ 0 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U62(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = 2 a__U62(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U62(z, z') -{ 0 }-> 0 :|: z = 2, z' = 3, v0 >= 0, 2 = v0 a__U62(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0 a__U62(z, z') -{ 0 }-> 0 :|: z = 2, z0 >= 0, z' = z0, v0 >= 0, 0 = v0 a__U62(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 3, 2 = z0, z0 >= 0 a__U62(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0 a__U62(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z0 >= 0, z' = z0, 0 = z0', z0' >= 0 a__U62(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U63(z) -{ 0 }-> 2 :|: z = 2 a__U63(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U63(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U71(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U71(z, z') -{ 0 }-> 1 + a__length(mark(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U71(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U81(z) -{ 0 }-> 1 :|: z = 2 a__U81(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U81(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> 1 + mark(z2) + (1 + z1 + z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U91(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__and(z, z') -{ 0 }-> mark(z0) :|: z = 2, z0 >= 0, z' = z0 a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__isNatKind(z02404), 1 + z02404) :|: z02404 >= 0, z = 1 + (1 + z02404) a__isNat(z) -{ 0 }-> a__U21(a__isNatIListKind(z02403), 1 + z02403) :|: z02403 >= 0, z = 1 + (1 + z02403) a__isNat(z) -{ 0 }-> a__U21(2, 0) :|: z = 1 + 0 a__isNat(z) -{ 0 }-> a__U21(0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U21(1 + z0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__and(a__isNatKind(z02401), 1 + z11201), 1 + z02401 + z11201) :|: z = 1 + (1 + z02401 + z11201), z02401 >= 0, z11201 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__and(a__isNatKind(z02402), 1 + z11202), 1 + z02402 + z11202) :|: z02402 >= 0, z11202 >= 0, z = 1 + (1 + z02402 + z11202) a__isNat(z) -{ 0 }-> a__U11(2, 3) :|: z = 1 + 3 a__isNat(z) -{ 0 }-> a__U11(2, 1) :|: z = 1 + 1 a__isNat(z) -{ 0 }-> a__U11(0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(1 + z0, z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> 2 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> a__U41(a__and(a__isNatKind(z02408), 1 + z1), 1 + z02408, z1) :|: z1 >= 0, z02408 >= 0, z = 1 + (1 + z02408) + z1 a__isNatIList(z) -{ 0 }-> a__U41(a__and(a__isNatIListKind(z02407), 1 + z1), 1 + z02407, z1) :|: z = 1 + (1 + z02407) + z1, z1 >= 0, z02407 >= 0 a__isNatIList(z) -{ 0 }-> a__U41(a__and(2, 1 + z1), 0, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatIList(z) -{ 0 }-> a__U41(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIList(z) -{ 0 }-> a__U41(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIList(z) -{ 0 }-> a__U31(a__and(a__isNatKind(z02405), 1 + z11203), 1 + z02405 + z11203) :|: z02405 >= 0, z11203 >= 0, z = 1 + z02405 + z11203 a__isNatIList(z) -{ 0 }-> a__U31(a__and(a__isNatKind(z02406), 1 + z11204), 1 + z02406 + z11204) :|: z02406 >= 0, z11204 >= 0, z = 1 + z02406 + z11204 a__isNatIList(z) -{ 0 }-> a__U31(2, 3) :|: z = 3 a__isNatIList(z) -{ 0 }-> a__U31(2, 1) :|: z = 1 a__isNatIList(z) -{ 0 }-> a__U31(0, z0) :|: z = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> a__U31(1 + z0, z0) :|: z = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> 2 :|: z = 3 a__isNatIList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatIList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatKind(z02410), 1 + z1) :|: z1 >= 0, z = 1 + (1 + z02410) + z1, z02410 >= 0 a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatKind(z02412), 1 + z1) :|: z1 >= 0, z02412 >= 0, z = 1 + (1 + z02412) + z1 a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatIListKind(z02409), 1 + z1) :|: z = 1 + (1 + z02409) + z1, z1 >= 0, z02409 >= 0 a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatIListKind(z02411), 1 + z1) :|: z = 1 + (1 + z02411) + z1, z1 >= 0, z02411 >= 0 a__isNatIListKind(z) -{ 0 }-> a__and(2, 1 + z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatIListKind(z) -{ 0 }-> a__and(0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIListKind(z) -{ 0 }-> a__and(1 + z0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 1 a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 3 a__isNatIListKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatIListKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__isNatIListKind(z0) :|: z = 1 + z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> 2 :|: z = 0 a__isNatKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__and(a__isNatKind(z02416), 1 + z1), 1 + z02416, z1) :|: z1 >= 0, z = 1 + (1 + z02416) + z1, z02416 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__and(a__isNatIListKind(z02415), 1 + z1), 1 + z02415, z1) :|: z1 >= 0, z = 1 + (1 + z02415) + z1, z02415 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__and(2, 1 + z1), 0, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatList(z) -{ 0 }-> a__U61(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U61(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U51(a__and(a__isNatKind(z02414), 1 + z1), 1 + z02414, z1) :|: z1 >= 0, z = 1 + (1 + z02414) + z1, z02414 >= 0 a__isNatList(z) -{ 0 }-> a__U51(a__and(a__isNatIListKind(z02413), 1 + z1), 1 + z02413, z1) :|: z = 1 + (1 + z02413) + z1, z02413 >= 0, z1 >= 0 a__isNatList(z) -{ 0 }-> a__U51(a__and(2, 1 + z1), 0, z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNatList(z) -{ 0 }-> a__U51(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U51(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> 2 :|: z = 1 a__isNatList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__length(z) -{ 0 }-> a__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z02418), 1 + z11206), z02418, z11206), 1 + (1 + z02418 + z11206)), 1 + (1 + z0) + (1 + z0)), 1 + z02418 + z11206) :|: z02418 >= 0, z11206 >= 0, z0 >= 0, z = 1 + z0 + (1 + z02418 + z11206) a__length(z) -{ 0 }-> a__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z02417), 1 + z11205), z02417, z11205), 1 + (1 + z02417 + z11205)), 1 + (1 + z0) + (1 + z0)), 1 + z02417 + z11205) :|: z02417 >= 0, z11205 >= 0, z0 >= 0, z = 1 + z0 + (1 + z02417 + z11205) a__length(z) -{ 0 }-> a__U71(a__and(a__and(2, 1 + 1), 1 + (1 + z0) + (1 + z0)), 1) :|: z0 >= 0, z = 1 + z0 + 1 a__length(z) -{ 0 }-> a__U71(a__and(a__and(0, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> a__U71(a__and(a__and(1 + z1, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> 0 :|: z = 1 a__length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__length(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z02420), 1 + z11208), z02420, z11208), 1 + (1 + z02420 + z11208)), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))), 1 + z02420 + z11208, z0, z1) :|: z11208 >= 0, z1 >= 0, z' = 1 + z1 + (1 + z02420 + z11208), z02420 >= 0, z = 1 + z0, z0 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(a__U31(a__isNatIListKind(z2), z2), 1 + z2), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))), z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(2, 1 + 3), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))), 3, z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1 + 3 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(0, 1 + z2), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))), z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(1 + z2, 1 + z2), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))), z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U81(a__and(a__U41(a__and(a__isNatKind(z02419), 1 + z11207), z02419, z11207), 1 + (1 + z02419 + z11207))) :|: z11207 >= 0, z02419 >= 0, z' = 1 + z02419 + z11207, z = 0 a__take(z, z') -{ 0 }-> a__U81(a__and(a__U31(a__isNatIListKind(z0), z0), 1 + z0)) :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> a__U81(a__and(2, 1 + 3)) :|: z' = 3, z = 0 a__take(z, z') -{ 0 }-> a__U81(a__and(0, 1 + z0)) :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> a__U81(a__and(1 + z0, 1 + z0)) :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__take(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__length(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatList(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatIListKind(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatIList(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__and(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U91(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U81(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U71(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U63(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U62(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U61(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U53(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U52(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U51(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U43(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U42(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U41(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U32(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U22(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U21(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U12(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U11(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 3 :|: z = 3 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 0 :|: z = 3 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + 0 + 3 :|: z = 3 ---------------------------------------- (57) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (58) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 1 }-> 1 + MARK(z') :|: z = 2, z' >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z - 2), 1 + (z - 2)) + A__ISNATKIND(1 + (z - 2)) :|: z - 2 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatIListKind(z - 2), 1 + (z - 2)) + A__ISNATKIND(1 + (z - 2)) :|: z - 2 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(2, 0) + A__ISNATKIND(0) :|: z = 1 + 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(0, z - 1) + A__ISNATKIND(z - 1) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(1 + (z - 1), z - 1) + A__ISNATKIND(z - 1) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z033), 1 + z113), 1 + z033 + z113) + A__ISNATILISTKIND(1 + z033 + z113) :|: z = 1 + (1 + z033 + z113), z033 >= 0, z113 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__and(a__isNatKind(z034), 1 + z114), 1 + z034 + z114) + A__ISNATILISTKIND(1 + z034 + z114) :|: z114 >= 0, z034 >= 0, z = 1 + (1 + z034 + z114) A__ISNAT(z) -{ 1 }-> 1 + A__U11(2, 3) + A__ISNATILISTKIND(3) :|: z = 1 + 3 A__ISNAT(z) -{ 1 }-> 1 + A__U11(2, 1) + A__ISNATILISTKIND(1) :|: z = 1 + 1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(0, z - 1) + A__ISNATILISTKIND(z - 1) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(1 + (z - 1), z - 1) + A__ISNATILISTKIND(z - 1) :|: z - 1 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(a__and(a__isNatKind(z037), 1 + z115), 1 + z037 + z115) + A__ISNATILISTKIND(1 + z037 + z115) :|: z115 >= 0, z = 1 + z037 + z115, z037 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(a__and(a__isNatKind(z038), 1 + z116), 1 + z038 + z116) + A__ISNATILISTKIND(1 + z038 + z116) :|: z = 1 + z038 + z116, z038 >= 0, z116 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(2, 3) + A__ISNATILISTKIND(3) :|: z = 3 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(2, 1) + A__ISNATILISTKIND(1) :|: z = 1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(0, z) + A__ISNATILISTKIND(z) :|: z >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(1 + z, z) + A__ISNATILISTKIND(z) :|: z >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z040), 1 + z1), 1 + z040, z1) + A__AND(a__isNatKind(z040), 1 + z1) + A__ISNATKIND(1 + z040) :|: z1 >= 0, z040 >= 0, z = 1 + (1 + z040) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z040), 1 + z1), 1 + z040, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z040) :|: z1 >= 0, z040 >= 0, z = 1 + (1 + z040) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z040), 1 + z1), 1 + z040, z1) + A__AND(1 + (1 + z040), 1 + z1) + A__ISNATKIND(1 + z040) :|: z1 >= 0, z040 >= 0, z = 1 + (1 + z040) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z039), 1 + z1), 1 + z039, z1) + A__AND(a__isNatIListKind(z039), 1 + z1) + A__ISNATKIND(1 + z039) :|: z1 >= 0, z039 >= 0, z = 1 + (1 + z039) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z039), 1 + z1), 1 + z039, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z039) :|: z1 >= 0, z039 >= 0, z = 1 + (1 + z039) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatIListKind(z039), 1 + z1), 1 + z039, z1) + A__AND(1 + (1 + z039), 1 + z1) + A__ISNATKIND(1 + z039) :|: z1 >= 0, z039 >= 0, z = 1 + (1 + z039) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(0, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(1 + 0, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 1 + z043, z1) + A__AND(a__isNatIListKind(z043), 1 + z1) + A__ISNATKIND(1 + z043) :|: z1 >= 0, z043 >= 0, z = 1 + (1 + z043) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + z1), 1 + z044, z1) + A__AND(a__isNatKind(z044), 1 + z1) + A__ISNATKIND(1 + z044) :|: z1 >= 0, z044 >= 0, z = 1 + (1 + z044) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(0, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + 0, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + (1 + z041), 1 + z1), 1 + z041, z1) + A__AND(a__isNatIListKind(z041), 1 + z1) + A__ISNATKIND(1 + z041) :|: z1 >= 0, z041 >= 0, z = 1 + (1 + z041) + z1 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(1 + (1 + z042), 1 + z1), 1 + z042, z1) + A__AND(a__isNatKind(z042), 1 + z1) + A__ISNATKIND(1 + z042) :|: z042 >= 0, z1 >= 0, z = 1 + (1 + z042) + z1 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z046), 1 + z1) + A__ISNATKIND(1 + z046) :|: z = 1 + (1 + z046) + z1, z046 >= 0, z1 >= 0 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z048), 1 + z1) + A__ISNATKIND(1 + z048) :|: z1 >= 0, z = 1 + (1 + z048) + z1, z048 >= 0 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatIListKind(z045), 1 + z1) + A__ISNATKIND(1 + z045) :|: z1 >= 0, z045 >= 0, z = 1 + (1 + z045) + z1 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatIListKind(z047), 1 + z1) + A__ISNATKIND(1 + z047) :|: z1 >= 0, z = 1 + (1 + z047) + z1, z047 >= 0 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z - 1) :|: z - 1 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z - 1) :|: z - 1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatKind(z056), 1 + z1), 1 + z056, z1) + A__AND(a__isNatKind(z056), 1 + z1) + A__ISNATKIND(1 + z056) :|: z056 >= 0, z1 >= 0, z = 1 + (1 + z056) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatKind(z056), 1 + z1), 1 + z056, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z056) :|: z056 >= 0, z1 >= 0, z = 1 + (1 + z056) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatKind(z056), 1 + z1), 1 + z056, z1) + A__AND(1 + (1 + z056), 1 + z1) + A__ISNATKIND(1 + z056) :|: z056 >= 0, z1 >= 0, z = 1 + (1 + z056) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatIListKind(z055), 1 + z1), 1 + z055, z1) + A__AND(a__isNatIListKind(z055), 1 + z1) + A__ISNATKIND(1 + z055) :|: z1 >= 0, z055 >= 0, z = 1 + (1 + z055) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatIListKind(z055), 1 + z1), 1 + z055, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z055) :|: z1 >= 0, z055 >= 0, z = 1 + (1 + z055) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatIListKind(z055), 1 + z1), 1 + z055, z1) + A__AND(1 + (1 + z055), 1 + z1) + A__ISNATKIND(1 + z055) :|: z1 >= 0, z055 >= 0, z = 1 + (1 + z055) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(0, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(1 + 0, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + z1), 1 + z059, z1) + A__AND(a__isNatIListKind(z059), 1 + z1) + A__ISNATKIND(1 + z059) :|: z = 1 + (1 + z059) + z1, z1 >= 0, z059 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + z1), 1 + z060, z1) + A__AND(a__isNatKind(z060), 1 + z1) + A__ISNATKIND(1 + z060) :|: z1 >= 0, z = 1 + (1 + z060) + z1, z060 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(0, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + 0, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + (1 + z057), 1 + z1), 1 + z057, z1) + A__AND(a__isNatIListKind(z057), 1 + z1) + A__ISNATKIND(1 + z057) :|: z1 >= 0, z = 1 + (1 + z057) + z1, z057 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(1 + (1 + z058), 1 + z1), 1 + z058, z1) + A__AND(a__isNatKind(z058), 1 + z1) + A__ISNATKIND(1 + z058) :|: z1 >= 0, z058 >= 0, z = 1 + (1 + z058) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z050), 1 + z1), 1 + z050, z1) + A__AND(a__isNatKind(z050), 1 + z1) + A__ISNATKIND(1 + z050) :|: z1 >= 0, z = 1 + (1 + z050) + z1, z050 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z050), 1 + z1), 1 + z050, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z050) :|: z1 >= 0, z = 1 + (1 + z050) + z1, z050 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z050), 1 + z1), 1 + z050, z1) + A__AND(1 + (1 + z050), 1 + z1) + A__ISNATKIND(1 + z050) :|: z1 >= 0, z = 1 + (1 + z050) + z1, z050 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z049), 1 + z1), 1 + z049, z1) + A__AND(a__isNatIListKind(z049), 1 + z1) + A__ISNATKIND(1 + z049) :|: z1 >= 0, z049 >= 0, z = 1 + (1 + z049) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z049), 1 + z1), 1 + z049, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(1 + z049) :|: z1 >= 0, z049 >= 0, z = 1 + (1 + z049) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatIListKind(z049), 1 + z1), 1 + z049, z1) + A__AND(1 + (1 + z049), 1 + z1) + A__ISNATKIND(1 + z049) :|: z1 >= 0, z049 >= 0, z = 1 + (1 + z049) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(0, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(2, 1 + (z - 1)), 0, z - 1) + A__AND(1 + 0, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 1 + z053, z1) + A__AND(a__isNatIListKind(z053), 1 + z1) + A__ISNATKIND(1 + z053) :|: z1 >= 0, z053 >= 0, z = 1 + (1 + z053) + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + z1), 1 + z054, z1) + A__AND(a__isNatKind(z054), 1 + z1) + A__ISNATKIND(1 + z054) :|: z = 1 + (1 + z054) + z1, z1 >= 0, z054 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(0, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + z0, 1 + z1), z0, z1) + A__AND(1 + z0, 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + 0, 1 + (z - 1)), 0, z - 1) + A__AND(2, 1 + (z - 1)) + A__ISNATKIND(0) :|: z - 1 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + (1 + z051), 1 + z1), 1 + z051, z1) + A__AND(a__isNatIListKind(z051), 1 + z1) + A__ISNATKIND(1 + z051) :|: z1 >= 0, z = 1 + (1 + z051) + z1, z051 >= 0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(1 + (1 + z052), 1 + z1), 1 + z052, z1) + A__AND(a__isNatKind(z052), 1 + z1) + A__ISNATKIND(1 + z052) :|: z = 1 + (1 + z052) + z1, z052 >= 0, z1 >= 0 A__LENGTH(z) -{ 1 }-> 1 + A__U71(a__and(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) + A__AND(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)) + A__AND(a__isNatList(z1), 1 + z1) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(a__U41(a__and(a__isNatKind(z02356), 1 + z11178), z02356, z11178), 1 + (1 + z02356 + z11178)) + A__ISNATILIST(1 + z02356 + z11178) :|: z' = 1 + z02356 + z11178, z11178 >= 0, z = 0, z02356 >= 0 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(a__U31(a__isNatIListKind(z'), z'), 1 + z') + A__ISNATILIST(z') :|: z' >= 0, z = 0 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(2, 1 + 3) + A__ISNATILIST(3) :|: z' = 3, z = 0 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(0, 1 + z') + A__ISNATILIST(z') :|: z' >= 0, z = 0 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(1 + z', 1 + z') + A__ISNATILIST(z') :|: z' >= 0, z = 0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(a__and(a__and(a__isNatIList(z2), 1 + z2), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + z1) + (1 + z1))), z2, z - 1, z1) + A__AND(a__and(a__isNatIList(z2), 1 + z2), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + z1) + (1 + z1))) + A__AND(a__isNatIList(z2), 1 + z2) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 A__U11(z, z') -{ 1 }-> 1 + A__ISNATLIST(z') :|: z = 2, z' >= 0 A__U21(z, z') -{ 1 }-> 1 + A__ISNAT(z') :|: z = 2, z' >= 0 A__U31(z, z') -{ 1 }-> 1 + A__ISNATLIST(z') :|: z = 2, z' >= 0 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U21(a__isNatKind(z' - 1), z' - 1), z'') + A__ISNAT(1 + (z' - 1)) :|: z = 2, z'' >= 0, z' - 1 >= 0 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') + A__ISNAT(1 + (z' - 1)) :|: z = 2, z'' >= 0, z' - 1 >= 0 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(2, z'') + A__ISNAT(0) :|: z = 2, z'' >= 0, z' = 0 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(0, z'') + A__ISNAT(z') :|: z = 2, z'' >= 0, z' >= 0 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(1 + z', z'') + A__ISNAT(z') :|: z = 2, z'' >= 0, z' >= 0 A__U42(z, z') -{ 1 }-> 1 + A__ISNATILIST(z') :|: z = 2, z' >= 0 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__U21(a__isNatKind(z' - 1), z' - 1), z'') + A__ISNAT(1 + (z' - 1)) :|: z = 2, z'' >= 0, z' - 1 >= 0 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') + A__ISNAT(1 + (z' - 1)) :|: z = 2, z'' >= 0, z' - 1 >= 0 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(2, z'') + A__ISNAT(0) :|: z = 2, z'' >= 0, z' = 0 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(0, z'') + A__ISNAT(z') :|: z = 2, z'' >= 0, z' >= 0 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(1 + z', z'') + A__ISNAT(z') :|: z = 2, z'' >= 0, z' >= 0 A__U52(z, z') -{ 1 }-> 1 + A__ISNATLIST(z') :|: z = 2, z' >= 0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(a__U21(a__isNatKind(z' - 1), z' - 1), z'') + A__ISNAT(1 + (z' - 1)) :|: z = 2, z' - 1 >= 0, z'' >= 0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') + A__ISNAT(1 + (z' - 1)) :|: z = 2, z'' >= 0, z' - 1 >= 0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(2, z'') + A__ISNAT(0) :|: z = 2, z'' >= 0, z' = 0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(0, z'') + A__ISNAT(z') :|: z = 2, z'' >= 0, z' >= 0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(1 + z', z'') + A__ISNAT(z') :|: z = 2, z'' >= 0, z' >= 0 A__U62(z, z') -{ 1 }-> 1 + A__ISNATILIST(z') :|: z = 2, z' >= 0 A__U71(z, z') -{ 1 }-> 1 + A__LENGTH(mark(z')) + MARK(z') :|: z = 2, z' >= 0 A__U91(z, z', z'', z4) -{ 1 }-> 1 + MARK(z4) :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATLIST(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATILIST(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__U91(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U71(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U62(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U52(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U42(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__LENGTH(mark(z - 1)) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__U11(z, z') -{ 0 }-> a__U12(a__U61(a__and(a__isNatKind(z02358), 1 + z11180), z02358, z11180)) :|: z = 2, z11180 >= 0, z' = 1 + z02358 + z11180, z02358 >= 0 a__U11(z, z') -{ 0 }-> a__U12(a__U51(a__and(a__isNatKind(z02357), 1 + z11179), z02357, z11179)) :|: z = 2, z' = 1 + z02357 + z11179, z11179 >= 0, z02357 >= 0 a__U11(z, z') -{ 0 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U11(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U11(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U11(z, z') -{ 0 }-> 0 :|: z = 2, z' = 1, v0 >= 0, 2 = v0 a__U11(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 1 + z' = v0 a__U11(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 0 = v0 a__U11(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 1, 2 = z0, z0 >= 0 a__U11(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 1 + z' = z0', z0' >= 0 a__U11(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 0 = z0', z0' >= 0 a__U11(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U12(z) -{ 0 }-> 2 :|: z = 2 a__U12(z) -{ 0 }-> 0 :|: z >= 0 a__U12(z) -{ 0 }-> 1 + z :|: z >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U21(a__isNatKind(z' - 1), z' - 1)) :|: z = 2, z' - 1 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__U11(a__isNatIListKind(z' - 1), z' - 1)) :|: z = 2, z' - 1 >= 0 a__U21(z, z') -{ 0 }-> 2 :|: z = 2, z' = 0, 2 = 2 a__U21(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U21(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U21(z, z') -{ 0 }-> 0 :|: z = 2, z' = 0, v0 >= 0, 2 = v0 a__U21(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 1 + z' = v0 a__U21(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 0 = v0 a__U21(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 0, 2 = z0, z0 >= 0 a__U21(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 1 + z' = z0', z0' >= 0 a__U21(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 0 = z0', z0' >= 0 a__U21(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U22(z) -{ 0 }-> 2 :|: z = 2 a__U22(z) -{ 0 }-> 0 :|: z >= 0 a__U22(z) -{ 0 }-> 1 + z :|: z >= 0 a__U31(z, z') -{ 0 }-> a__U32(a__U61(a__and(a__isNatKind(z02362), 1 + z11182), z02362, z11182)) :|: z = 2, z02362 >= 0, z' = 1 + z02362 + z11182, z11182 >= 0 a__U31(z, z') -{ 0 }-> a__U32(a__U51(a__and(a__isNatKind(z02361), 1 + z11181), z02361, z11181)) :|: z = 2, z11181 >= 0, z02361 >= 0, z' = 1 + z02361 + z11181 a__U31(z, z') -{ 0 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U31(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U31(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U31(z, z') -{ 0 }-> 0 :|: z = 2, z' = 1, v0 >= 0, 2 = v0 a__U31(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 1 + z' = v0 a__U31(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 0 = v0 a__U31(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 1, 2 = z0, z0 >= 0 a__U31(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 1 + z' = z0', z0' >= 0 a__U31(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 0 = z0', z0' >= 0 a__U31(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U32(z) -{ 0 }-> 2 :|: z = 2 a__U32(z) -{ 0 }-> 0 :|: z >= 0 a__U32(z) -{ 0 }-> 1 + z :|: z >= 0 a__U41(z, z', z'') -{ 0 }-> a__U42(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0 a__U41(z, z', z'') -{ 0 }-> a__U42(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0 a__U41(z, z', z'') -{ 0 }-> a__U42(2, z'') :|: z = 2, z'' >= 0, z' = 0 a__U41(z, z', z'') -{ 0 }-> a__U42(0, z'') :|: z = 2, z'' >= 0, z' >= 0 a__U41(z, z', z'') -{ 0 }-> a__U42(1 + z', z'') :|: z = 2, z'' >= 0, z' >= 0 a__U41(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U41(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__U42(z, z') -{ 0 }-> a__U43(a__U41(a__and(a__isNatKind(z02365), 1 + z11183), z02365, z11183)) :|: z = 2, z11183 >= 0, z02365 >= 0, z' = 1 + z02365 + z11183 a__U42(z, z') -{ 0 }-> a__U43(a__U31(a__isNatIListKind(z'), z')) :|: z = 2, z' >= 0 a__U42(z, z') -{ 0 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U42(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U42(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U42(z, z') -{ 0 }-> 0 :|: z = 2, z' = 3, v0 >= 0, 2 = v0 a__U42(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 1 + z' = v0 a__U42(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 0 = v0 a__U42(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 3, 2 = z0, z0 >= 0 a__U42(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 1 + z' = z0', z0' >= 0 a__U42(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 0 = z0', z0' >= 0 a__U42(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U43(z) -{ 0 }-> 2 :|: z = 2 a__U43(z) -{ 0 }-> 0 :|: z >= 0 a__U43(z) -{ 0 }-> 1 + z :|: z >= 0 a__U51(z, z', z'') -{ 0 }-> a__U52(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0 a__U51(z, z', z'') -{ 0 }-> a__U52(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') :|: z = 2, z' - 1 >= 0, z'' >= 0 a__U51(z, z', z'') -{ 0 }-> a__U52(2, z'') :|: z = 2, z'' >= 0, z' = 0 a__U51(z, z', z'') -{ 0 }-> a__U52(0, z'') :|: z = 2, z'' >= 0, z' >= 0 a__U51(z, z', z'') -{ 0 }-> a__U52(1 + z', z'') :|: z = 2, z'' >= 0, z' >= 0 a__U51(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U51(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__U52(z, z') -{ 0 }-> a__U53(a__U61(a__and(a__isNatKind(z02369), 1 + z11185), z02369, z11185)) :|: z = 2, z11185 >= 0, z02369 >= 0, z' = 1 + z02369 + z11185 a__U52(z, z') -{ 0 }-> a__U53(a__U51(a__and(a__isNatKind(z02368), 1 + z11184), z02368, z11184)) :|: z = 2, z' = 1 + z02368 + z11184, z11184 >= 0, z02368 >= 0 a__U52(z, z') -{ 0 }-> 2 :|: z = 2, z' = 1, 2 = 2 a__U52(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U52(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U52(z, z') -{ 0 }-> 0 :|: z = 2, z' = 1, v0 >= 0, 2 = v0 a__U52(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 1 + z' = v0 a__U52(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 0 = v0 a__U52(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 1, 2 = z0, z0 >= 0 a__U52(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 1 + z' = z0', z0' >= 0 a__U52(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 0 = z0', z0' >= 0 a__U52(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U53(z) -{ 0 }-> 2 :|: z = 2 a__U53(z) -{ 0 }-> 0 :|: z >= 0 a__U53(z) -{ 0 }-> 1 + z :|: z >= 0 a__U61(z, z', z'') -{ 0 }-> a__U62(a__U21(a__isNatKind(z' - 1), z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0 a__U61(z, z', z'') -{ 0 }-> a__U62(a__U11(a__isNatIListKind(z' - 1), z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0 a__U61(z, z', z'') -{ 0 }-> a__U62(2, z'') :|: z = 2, z'' >= 0, z' = 0 a__U61(z, z', z'') -{ 0 }-> a__U62(0, z'') :|: z = 2, z'' >= 0, z' >= 0 a__U61(z, z', z'') -{ 0 }-> a__U62(1 + z', z'') :|: z = 2, z'' >= 0, z' >= 0 a__U61(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U61(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 a__U62(z, z') -{ 0 }-> a__U63(a__U41(a__and(a__isNatKind(z02372), 1 + z11186), z02372, z11186)) :|: z = 2, z02372 >= 0, z11186 >= 0, z' = 1 + z02372 + z11186 a__U62(z, z') -{ 0 }-> a__U63(a__U31(a__isNatIListKind(z'), z')) :|: z = 2, z' >= 0 a__U62(z, z') -{ 0 }-> 2 :|: z = 2, z' = 3, 2 = 2 a__U62(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0, 1 + z' = 2 a__U62(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U62(z, z') -{ 0 }-> 0 :|: z = 2, z' = 3, v0 >= 0, 2 = v0 a__U62(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 1 + z' = v0 a__U62(z, z') -{ 0 }-> 0 :|: z = 2, z' >= 0, v0 >= 0, 0 = v0 a__U62(z, z') -{ 0 }-> 1 + z0 :|: z = 2, z' = 3, 2 = z0, z0 >= 0 a__U62(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 1 + z' = z0', z0' >= 0 a__U62(z, z') -{ 0 }-> 1 + z0' :|: z = 2, z' >= 0, 0 = z0', z0' >= 0 a__U62(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U63(z) -{ 0 }-> 2 :|: z = 2 a__U63(z) -{ 0 }-> 0 :|: z >= 0 a__U63(z) -{ 0 }-> 1 + z :|: z >= 0 a__U71(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U71(z, z') -{ 0 }-> 1 + a__length(mark(z')) :|: z = 2, z' >= 0 a__U71(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U81(z) -{ 0 }-> 1 :|: z = 2 a__U81(z) -{ 0 }-> 0 :|: z >= 0 a__U81(z) -{ 0 }-> 1 + z :|: z >= 0 a__U91(z, z', z'', z4) -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0, z4 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> 1 + mark(z4) + (1 + z'' + z') :|: z = 2, z'' >= 0, z' >= 0, z4 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> 1 + z + z' + z'' + z4 :|: z' >= 0, z >= 0, z'' >= 0, z4 >= 0 a__and(z, z') -{ 0 }-> mark(z') :|: z = 2, z' >= 0 a__and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__and(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__isNat(z) -{ 0 }-> a__U21(a__isNatKind(z - 2), 1 + (z - 2)) :|: z - 2 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__isNatIListKind(z - 2), 1 + (z - 2)) :|: z - 2 >= 0 a__isNat(z) -{ 0 }-> a__U21(2, 0) :|: z = 1 + 0 a__isNat(z) -{ 0 }-> a__U21(0, z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 0 }-> a__U21(1 + (z - 1), z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__and(a__isNatKind(z02401), 1 + z11201), 1 + z02401 + z11201) :|: z = 1 + (1 + z02401 + z11201), z02401 >= 0, z11201 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__and(a__isNatKind(z02402), 1 + z11202), 1 + z02402 + z11202) :|: z02402 >= 0, z11202 >= 0, z = 1 + (1 + z02402 + z11202) a__isNat(z) -{ 0 }-> a__U11(2, 3) :|: z = 1 + 3 a__isNat(z) -{ 0 }-> a__U11(2, 1) :|: z = 1 + 1 a__isNat(z) -{ 0 }-> a__U11(0, z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 0 }-> a__U11(1 + (z - 1), z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 0 }-> 2 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: z >= 0 a__isNat(z) -{ 0 }-> 1 + z :|: z >= 0 a__isNatIList(z) -{ 0 }-> a__U41(a__and(a__isNatKind(z02408), 1 + z1), 1 + z02408, z1) :|: z1 >= 0, z02408 >= 0, z = 1 + (1 + z02408) + z1 a__isNatIList(z) -{ 0 }-> a__U41(a__and(a__isNatIListKind(z02407), 1 + z1), 1 + z02407, z1) :|: z = 1 + (1 + z02407) + z1, z1 >= 0, z02407 >= 0 a__isNatIList(z) -{ 0 }-> a__U41(a__and(2, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0 a__isNatIList(z) -{ 0 }-> a__U41(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIList(z) -{ 0 }-> a__U41(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIList(z) -{ 0 }-> a__U31(a__and(a__isNatKind(z02405), 1 + z11203), 1 + z02405 + z11203) :|: z02405 >= 0, z11203 >= 0, z = 1 + z02405 + z11203 a__isNatIList(z) -{ 0 }-> a__U31(a__and(a__isNatKind(z02406), 1 + z11204), 1 + z02406 + z11204) :|: z02406 >= 0, z11204 >= 0, z = 1 + z02406 + z11204 a__isNatIList(z) -{ 0 }-> a__U31(2, 3) :|: z = 3 a__isNatIList(z) -{ 0 }-> a__U31(2, 1) :|: z = 1 a__isNatIList(z) -{ 0 }-> a__U31(0, z) :|: z >= 0 a__isNatIList(z) -{ 0 }-> a__U31(1 + z, z) :|: z >= 0 a__isNatIList(z) -{ 0 }-> 2 :|: z = 3 a__isNatIList(z) -{ 0 }-> 0 :|: z >= 0 a__isNatIList(z) -{ 0 }-> 1 + z :|: z >= 0 a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatKind(z02410), 1 + z1) :|: z1 >= 0, z = 1 + (1 + z02410) + z1, z02410 >= 0 a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatKind(z02412), 1 + z1) :|: z1 >= 0, z02412 >= 0, z = 1 + (1 + z02412) + z1 a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatIListKind(z02409), 1 + z1) :|: z = 1 + (1 + z02409) + z1, z1 >= 0, z02409 >= 0 a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatIListKind(z02411), 1 + z1) :|: z = 1 + (1 + z02411) + z1, z1 >= 0, z02411 >= 0 a__isNatIListKind(z) -{ 0 }-> a__and(2, 1 + (z - 1)) :|: z - 1 >= 0 a__isNatIListKind(z) -{ 0 }-> a__and(0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIListKind(z) -{ 0 }-> a__and(1 + z0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 1 a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 3 a__isNatIListKind(z) -{ 0 }-> 0 :|: z >= 0 a__isNatIListKind(z) -{ 0 }-> 1 + z :|: z >= 0 a__isNatKind(z) -{ 0 }-> a__isNatKind(z - 1) :|: z - 1 >= 0 a__isNatKind(z) -{ 0 }-> a__isNatIListKind(z - 1) :|: z - 1 >= 0 a__isNatKind(z) -{ 0 }-> 2 :|: z = 0 a__isNatKind(z) -{ 0 }-> 0 :|: z >= 0 a__isNatKind(z) -{ 0 }-> 1 + z :|: z >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__and(a__isNatKind(z02416), 1 + z1), 1 + z02416, z1) :|: z1 >= 0, z = 1 + (1 + z02416) + z1, z02416 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__and(a__isNatIListKind(z02415), 1 + z1), 1 + z02415, z1) :|: z1 >= 0, z = 1 + (1 + z02415) + z1, z02415 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__and(2, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U61(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U51(a__and(a__isNatKind(z02414), 1 + z1), 1 + z02414, z1) :|: z1 >= 0, z = 1 + (1 + z02414) + z1, z02414 >= 0 a__isNatList(z) -{ 0 }-> a__U51(a__and(a__isNatIListKind(z02413), 1 + z1), 1 + z02413, z1) :|: z = 1 + (1 + z02413) + z1, z02413 >= 0, z1 >= 0 a__isNatList(z) -{ 0 }-> a__U51(a__and(2, 1 + (z - 1)), 0, z - 1) :|: z - 1 >= 0 a__isNatList(z) -{ 0 }-> a__U51(a__and(0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U51(a__and(1 + z0, 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> 2 :|: z = 1 a__isNatList(z) -{ 0 }-> 0 :|: z >= 0 a__isNatList(z) -{ 0 }-> 1 + z :|: z >= 0 a__length(z) -{ 0 }-> a__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z02418), 1 + z11206), z02418, z11206), 1 + (1 + z02418 + z11206)), 1 + (1 + z0) + (1 + z0)), 1 + z02418 + z11206) :|: z02418 >= 0, z11206 >= 0, z0 >= 0, z = 1 + z0 + (1 + z02418 + z11206) a__length(z) -{ 0 }-> a__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z02417), 1 + z11205), z02417, z11205), 1 + (1 + z02417 + z11205)), 1 + (1 + z0) + (1 + z0)), 1 + z02417 + z11205) :|: z02417 >= 0, z11205 >= 0, z0 >= 0, z = 1 + z0 + (1 + z02417 + z11205) a__length(z) -{ 0 }-> a__U71(a__and(a__and(2, 1 + 1), 1 + (1 + (z - 2)) + (1 + (z - 2))), 1) :|: z - 2 >= 0 a__length(z) -{ 0 }-> a__U71(a__and(a__and(0, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> a__U71(a__and(a__and(1 + z1, 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> 0 :|: z = 1 a__length(z) -{ 0 }-> 0 :|: z >= 0 a__length(z) -{ 0 }-> 1 + z :|: z >= 0 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z02420), 1 + z11208), z02420, z11208), 1 + (1 + z02420 + z11208)), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + z1) + (1 + z1))), 1 + z02420 + z11208, z - 1, z1) :|: z11208 >= 0, z1 >= 0, z' = 1 + z1 + (1 + z02420 + z11208), z02420 >= 0, z - 1 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(a__U31(a__isNatIListKind(z2), z2), 1 + z2), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + z1) + (1 + z1))), z2, z - 1, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(2, 1 + 3), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + (z' - 4)) + (1 + (z' - 4)))), 3, z - 1, z' - 4) :|: z' - 4 >= 0, z - 1 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(0, 1 + z2), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + z1) + (1 + z1))), z2, z - 1, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(1 + z2, 1 + z2), 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) + (1 + (1 + z1) + (1 + z1))), z2, z - 1, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U81(a__and(a__U41(a__and(a__isNatKind(z02419), 1 + z11207), z02419, z11207), 1 + (1 + z02419 + z11207))) :|: z11207 >= 0, z02419 >= 0, z' = 1 + z02419 + z11207, z = 0 a__take(z, z') -{ 0 }-> a__U81(a__and(a__U31(a__isNatIListKind(z'), z'), 1 + z')) :|: z' >= 0, z = 0 a__take(z, z') -{ 0 }-> a__U81(a__and(2, 1 + 3)) :|: z' = 3, z = 0 a__take(z, z') -{ 0 }-> a__U81(a__and(0, 1 + z')) :|: z' >= 0, z = 0 a__take(z, z') -{ 0 }-> a__U81(a__and(1 + z', 1 + z')) :|: z' >= 0, z = 0 a__take(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__take(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__length(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__isNatList(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__isNatKind(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__isNatIListKind(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__isNatIList(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__isNat(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__and(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U91(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U81(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U71(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U63(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U62(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U61(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U53(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U52(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U51(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U43(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U42(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U41(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U32(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U22(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U21(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U12(mark(z - 1)) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U11(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 3 :|: z = 3 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 0 :|: z = 3 mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + 0 + 3 :|: z = 3 ---------------------------------------- (59) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: a__zeros -> null_a__zeros [0] a__U11(v0, v1) -> null_a__U11 [0] a__U12(v0) -> null_a__U12 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0) -> null_a__U22 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U32(v0) -> null_a__U32 [0] a__U41(v0, v1, v2) -> null_a__U41 [0] a__U42(v0, v1) -> null_a__U42 [0] a__U43(v0) -> null_a__U43 [0] a__U51(v0, v1, v2) -> null_a__U51 [0] a__U52(v0, v1) -> null_a__U52 [0] a__U53(v0) -> null_a__U53 [0] a__U61(v0, v1, v2) -> null_a__U61 [0] a__U62(v0, v1) -> null_a__U62 [0] a__U63(v0) -> null_a__U63 [0] a__U71(v0, v1) -> null_a__U71 [0] a__U81(v0) -> null_a__U81 [0] a__U91(v0, v1, v2, v3) -> null_a__U91 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [0] a__isNatIList(v0) -> null_a__isNatIList [0] a__isNatIListKind(v0) -> null_a__isNatIListKind [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__isNatList(v0) -> null_a__isNatList [0] a__length(v0) -> null_a__length [0] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] A__U41(v0, v1, v2) -> null_A__U41 [0] A__U51(v0, v1, v2) -> null_A__U51 [0] A__U61(v0, v1, v2) -> null_A__U61 [0] A__U71(v0, v1) -> null_A__U71 [0] A__U91(v0, v1, v2, v3) -> null_A__U91 [0] A__AND(v0, v1) -> null_A__AND [0] A__ISNAT(v0) -> null_A__ISNAT [0] A__ISNATILISTKIND(v0) -> null_A__ISNATILISTKIND [0] A__ISNATKIND(v0) -> null_A__ISNATKIND [0] A__ISNATLIST(v0) -> null_A__ISNATLIST [0] A__LENGTH(v0) -> null_A__LENGTH [0] A__TAKE(v0, v1) -> null_A__TAKE [0] MARK(v0) -> null_MARK [0] A__U11(v0, v1) -> null_A__U11 [0] A__U21(v0, v1) -> null_A__U21 [0] A__U31(v0, v1) -> null_A__U31 [0] A__U42(v0, v1) -> null_A__U42 [0] A__U52(v0, v1) -> null_A__U52 [0] A__U62(v0, v1) -> null_A__U62 [0] And the following fresh constants: null_a__zeros, null_a__U11, null_a__U12, null_a__U21, null_a__U22, null_a__U31, null_a__U32, null_a__U41, null_a__U42, null_a__U43, null_a__U51, null_a__U52, null_a__U53, null_a__U61, null_a__U62, null_a__U63, null_a__U71, null_a__U81, null_a__U91, null_a__and, null_a__isNat, null_a__isNatIList, null_a__isNatIListKind, null_a__isNatKind, null_a__isNatList, null_a__length, null_a__take, null_mark, null_A__U41, null_A__U51, null_A__U61, null_A__U71, null_A__U91, null_A__AND, null_A__ISNAT, null_A__ISNATILISTKIND, null_A__ISNATKIND, null_A__ISNATLIST, null_A__LENGTH, null_A__TAKE, null_MARK, null_A__U11, null_A__U21, null_A__U31, null_A__U42, null_A__U52, null_A__U62, const ---------------------------------------- (60) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) [1] A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) [1] A__AND(tt, z0) -> c38(MARK(z0)) [1] A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1] A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) [1] A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) [1] A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) [1] A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) [1] A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) [1] A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) [1] MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) [1] MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c73(A__ISNAT(z0)) [1] MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) [1] MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) [1] MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) [1] MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) [1] MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) [1] MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) [1] MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) [1] MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) [1] MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) [1] MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) [1] MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) [1] MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) [1] MARK(cons(z0, z1)) -> c95(MARK(z0)) [1] MARK(s(z0)) -> c98(MARK(z0)) [1] A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) [1] A__U21(tt, z0) -> c6(A__ISNAT(z0)) [1] A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) [1] A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) [1] A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) [1] A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) [1] A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) [1] MARK(U12(z0)) -> c69(MARK(z0)) [1] MARK(U22(z0)) -> c72(MARK(z0)) [1] MARK(U32(z0)) -> c75(MARK(z0)) [1] MARK(U43(z0)) -> c78(MARK(z0)) [1] MARK(U53(z0)) -> c82(MARK(z0)) [1] MARK(U63(z0)) -> c85(MARK(z0)) [1] MARK(U81(z0)) -> c88(MARK(z0)) [1] a__zeros -> cons(0, zeros) [0] a__zeros -> zeros [0] a__U11(tt, z0) -> a__U12(a__isNatList(z0)) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U12(tt) -> tt [0] a__U12(z0) -> U12(z0) [0] a__U21(tt, z0) -> a__U22(a__isNat(z0)) [0] a__U21(z0, z1) -> U21(z0, z1) [0] a__U22(tt) -> tt [0] a__U22(z0) -> U22(z0) [0] a__U31(tt, z0) -> a__U32(a__isNatList(z0)) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U32(tt) -> tt [0] a__U32(z0) -> U32(z0) [0] a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) [0] a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0] a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) [0] a__U42(z0, z1) -> U42(z0, z1) [0] a__U43(tt) -> tt [0] a__U43(z0) -> U43(z0) [0] a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) [0] a__U51(z0, z1, z2) -> U51(z0, z1, z2) [0] a__U52(tt, z0) -> a__U53(a__isNatList(z0)) [0] a__U52(z0, z1) -> U52(z0, z1) [0] a__U53(tt) -> tt [0] a__U53(z0) -> U53(z0) [0] a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) [0] a__U61(z0, z1, z2) -> U61(z0, z1, z2) [0] a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) [0] a__U62(z0, z1) -> U62(z0, z1) [0] a__U63(tt) -> tt [0] a__U63(z0) -> U63(z0) [0] a__U71(tt, z0) -> s(a__length(mark(z0))) [0] a__U71(z0, z1) -> U71(z0, z1) [0] a__U81(tt) -> nil [0] a__U81(z0) -> U81(z0) [0] a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) [0] a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) [0] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__isNat(0) -> tt [0] a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) [0] a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) [0] a__isNat(z0) -> isNat(z0) [0] a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) [0] a__isNatIList(zeros) -> tt [0] a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatIList(z0) -> isNatIList(z0) [0] a__isNatIListKind(nil) -> tt [0] a__isNatIListKind(zeros) -> tt [0] a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) [0] a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) [0] a__isNatIListKind(z0) -> isNatIListKind(z0) [0] a__isNatKind(0) -> tt [0] a__isNatKind(length(z0)) -> a__isNatIListKind(z0) [0] a__isNatKind(s(z0)) -> a__isNatKind(z0) [0] a__isNatKind(z0) -> isNatKind(z0) [0] a__isNatList(nil) -> tt [0] a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) [0] a__isNatList(z0) -> isNatList(z0) [0] a__length(nil) -> 0 [0] a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) [0] a__length(z0) -> length(z0) [0] a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) [0] a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) [0] a__take(z0, z1) -> take(z0, z1) [0] mark(zeros) -> a__zeros [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U12(z0)) -> a__U12(mark(z0)) [0] mark(isNatList(z0)) -> a__isNatList(z0) [0] mark(U21(z0, z1)) -> a__U21(mark(z0), z1) [0] mark(U22(z0)) -> a__U22(mark(z0)) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U32(z0)) -> a__U32(mark(z0)) [0] mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0] mark(U42(z0, z1)) -> a__U42(mark(z0), z1) [0] mark(U43(z0)) -> a__U43(mark(z0)) [0] mark(isNatIList(z0)) -> a__isNatIList(z0) [0] mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) [0] mark(U52(z0, z1)) -> a__U52(mark(z0), z1) [0] mark(U53(z0)) -> a__U53(mark(z0)) [0] mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) [0] mark(U62(z0, z1)) -> a__U62(mark(z0), z1) [0] mark(U63(z0)) -> a__U63(mark(z0)) [0] mark(U71(z0, z1)) -> a__U71(mark(z0), z1) [0] mark(length(z0)) -> a__length(mark(z0)) [0] mark(U81(z0)) -> a__U81(mark(z0)) [0] mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) [0] mark(isNatKind(z0)) -> a__isNatKind(z0) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] a__zeros -> null_a__zeros [0] a__U11(v0, v1) -> null_a__U11 [0] a__U12(v0) -> null_a__U12 [0] a__U21(v0, v1) -> null_a__U21 [0] a__U22(v0) -> null_a__U22 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U32(v0) -> null_a__U32 [0] a__U41(v0, v1, v2) -> null_a__U41 [0] a__U42(v0, v1) -> null_a__U42 [0] a__U43(v0) -> null_a__U43 [0] a__U51(v0, v1, v2) -> null_a__U51 [0] a__U52(v0, v1) -> null_a__U52 [0] a__U53(v0) -> null_a__U53 [0] a__U61(v0, v1, v2) -> null_a__U61 [0] a__U62(v0, v1) -> null_a__U62 [0] a__U63(v0) -> null_a__U63 [0] a__U71(v0, v1) -> null_a__U71 [0] a__U81(v0) -> null_a__U81 [0] a__U91(v0, v1, v2, v3) -> null_a__U91 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [0] a__isNatIList(v0) -> null_a__isNatIList [0] a__isNatIListKind(v0) -> null_a__isNatIListKind [0] a__isNatKind(v0) -> null_a__isNatKind [0] a__isNatList(v0) -> null_a__isNatList [0] a__length(v0) -> null_a__length [0] a__take(v0, v1) -> null_a__take [0] mark(v0) -> null_mark [0] A__U41(v0, v1, v2) -> null_A__U41 [0] A__U51(v0, v1, v2) -> null_A__U51 [0] A__U61(v0, v1, v2) -> null_A__U61 [0] A__U71(v0, v1) -> null_A__U71 [0] A__U91(v0, v1, v2, v3) -> null_A__U91 [0] A__AND(v0, v1) -> null_A__AND [0] A__ISNAT(v0) -> null_A__ISNAT [0] A__ISNATILISTKIND(v0) -> null_A__ISNATILISTKIND [0] A__ISNATKIND(v0) -> null_A__ISNATKIND [0] A__ISNATLIST(v0) -> null_A__ISNATLIST [0] A__LENGTH(v0) -> null_A__LENGTH [0] A__TAKE(v0, v1) -> null_A__TAKE [0] MARK(v0) -> null_MARK [0] A__U11(v0, v1) -> null_A__U11 [0] A__U21(v0, v1) -> null_A__U21 [0] A__U31(v0, v1) -> null_A__U31 [0] A__U42(v0, v1) -> null_A__U42 [0] A__U52(v0, v1) -> null_A__U52 [0] A__U62(v0, v1) -> null_A__U62 [0] The TRS has the following type information: A__U41 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c14:null_A__U41 tt :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c14 :: c16:null_A__U42 -> c41:c42:null_A__ISNAT -> c14:null_A__U41 A__U42 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c16:null_A__U42 a__isNat :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark A__ISNAT :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c41:c42:null_A__ISNAT A__U51 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c20:null_A__U51 c20 :: c22:null_A__U52 -> c41:c42:null_A__ISNAT -> c20:null_A__U51 A__U52 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c22:null_A__U52 A__U61 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c26:null_A__U61 c26 :: c28:null_A__U62 -> c41:c42:null_A__ISNAT -> c26:null_A__U61 A__U62 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c28:null_A__U62 A__U71 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c32:null_A__U71 c32 :: c62:null_A__LENGTH -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c32:null_A__U71 A__LENGTH :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c62:null_A__LENGTH mark :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark MARK :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK A__U91 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c36:null_A__U91 c36 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c36:null_A__U91 A__AND :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c38:null_A__AND c38 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c38:null_A__AND length :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c41 :: c2:null_A__U11 -> c50:c51:null_A__ISNATILISTKIND -> c41:c42:null_A__ISNAT A__U11 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c2:null_A__U11 a__isNatIListKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark A__ISNATILISTKIND :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c50:c51:null_A__ISNATILISTKIND s :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c42 :: c6:null_A__U21 -> c54:c55:null_A__ISNATKIND -> c41:c42:null_A__ISNAT A__U21 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c6:null_A__U21 a__isNatKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark A__ISNATKIND :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c54:c55:null_A__ISNATKIND A__ISNATILIST :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c44:c46 c44 :: c10:null_A__U31 -> c50:c51:null_A__ISNATILISTKIND -> c44:c46 A__U31 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c10:null_A__U31 cons :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c46 :: c14:null_A__U41 -> c38:null_A__AND -> c54:c55:null_A__ISNATKIND -> c44:c46 a__and :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark isNatIListKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c50 :: c38:null_A__AND -> c54:c55:null_A__ISNATKIND -> c50:c51:null_A__ISNATILISTKIND take :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c51 :: c38:null_A__AND -> c54:c55:null_A__ISNATKIND -> c50:c51:null_A__ISNATILISTKIND c54 :: c50:c51:null_A__ISNATILISTKIND -> c54:c55:null_A__ISNATKIND c55 :: c54:c55:null_A__ISNATKIND -> c54:c55:null_A__ISNATKIND A__ISNATLIST :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c58:c59:null_A__ISNATLIST c58 :: c20:null_A__U51 -> c38:null_A__AND -> c54:c55:null_A__ISNATKIND -> c58:c59:null_A__ISNATLIST c59 :: c26:null_A__U61 -> c38:null_A__AND -> c54:c55:null_A__ISNATKIND -> c58:c59:null_A__ISNATLIST c62 :: c32:null_A__U71 -> c38:null_A__AND -> c38:null_A__AND -> c58:c59:null_A__ISNATLIST -> c62:null_A__LENGTH a__isNatList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark and :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark isNat :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark isNatKind :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark A__TAKE :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> c65:c64:null_A__TAKE c65 :: c36:null_A__U91 -> c38:null_A__AND -> c38:null_A__AND -> c44:c46 -> c65:c64:null_A__TAKE a__isNatIList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark U11 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c68 :: c2:null_A__U11 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK isNatList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c70 :: c58:c59:null_A__ISNATLIST -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U21 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c71 :: c6:null_A__U21 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK c73 :: c41:c42:null_A__ISNAT -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U31 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c74 :: c10:null_A__U31 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U41 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c76 :: c14:null_A__U41 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U42 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c77 :: c16:null_A__U42 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK isNatIList :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c79 :: c44:c46 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U51 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c80 :: c20:null_A__U51 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U52 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c81 :: c22:null_A__U52 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U61 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c83 :: c26:null_A__U61 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U62 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c84 :: c28:null_A__U62 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U71 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c86 :: c32:null_A__U71 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK c87 :: c62:null_A__LENGTH -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U91 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c89 :: c36:null_A__U91 -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK c90 :: c65:c64:null_A__TAKE -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK c91 :: c65:c64:null_A__TAKE -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK c92 :: c38:null_A__AND -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK c93 :: c50:c51:null_A__ISNATILISTKIND -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK c94 :: c54:c55:null_A__ISNATKIND -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK c95 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK c98 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK c2 :: c58:c59:null_A__ISNATLIST -> c2:null_A__U11 c6 :: c41:c42:null_A__ISNAT -> c6:null_A__U21 c10 :: c58:c59:null_A__ISNATLIST -> c10:null_A__U31 c16 :: c44:c46 -> c16:null_A__U42 c22 :: c58:c59:null_A__ISNATLIST -> c22:null_A__U52 c28 :: c44:c46 -> c28:null_A__U62 0 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c64 :: c38:null_A__AND -> c44:c46 -> c65:c64:null_A__TAKE U12 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c69 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U22 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c72 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U32 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c75 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U43 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c78 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U53 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c82 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U63 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark c85 :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK -> c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK U81 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark -> 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tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U81 :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__U91 :: 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tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__length :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_a__take :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_mark :: tt:length:s:cons:isNatIListKind:take:isNat:isNatKind:and:U11:isNatList:U21:U31:U41:U42:isNatIList:U51:U52:U61:U62:U71:U91:0:U12:U22:U32:U43:U53:U63:U81:zeros:nil:null_a__zeros:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__U31:null_a__U32:null_a__U41:null_a__U42:null_a__U43:null_a__U51:null_a__U52:null_a__U53:null_a__U61:null_a__U62:null_a__U63:null_a__U71:null_a__U81:null_a__U91:null_a__and:null_a__isNat:null_a__isNatIList:null_a__isNatIListKind:null_a__isNatKind:null_a__isNatList:null_a__length:null_a__take:null_mark null_A__U41 :: c14:null_A__U41 null_A__U51 :: c20:null_A__U51 null_A__U61 :: c26:null_A__U61 null_A__U71 :: c32:null_A__U71 null_A__U91 :: c36:null_A__U91 null_A__AND :: c38:null_A__AND null_A__ISNAT :: c41:c42:null_A__ISNAT null_A__ISNATILISTKIND :: c50:c51:null_A__ISNATILISTKIND null_A__ISNATKIND :: c54:c55:null_A__ISNATKIND null_A__ISNATLIST :: c58:c59:null_A__ISNATLIST null_A__LENGTH :: c62:null_A__LENGTH null_A__TAKE :: c65:c64:null_A__TAKE null_MARK :: c68:c70:c71:c73:c74:c76:c77:c79:c80:c81:c83:c84:c86:c87:c89:c90:c91:c92:c93:c94:c95:c98:c69:c72:c75:c78:c82:c85:c88:null_MARK null_A__U11 :: c2:null_A__U11 null_A__U21 :: c6:null_A__U21 null_A__U31 :: c10:null_A__U31 null_A__U42 :: c16:null_A__U42 null_A__U52 :: c22:null_A__U52 null_A__U62 :: c28:null_A__U62 const :: c44:c46 Rewrite Strategy: INNERMOST ---------------------------------------- (61) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 2 0 => 0 zeros => 3 nil => 1 null_a__zeros => 0 null_a__U11 => 0 null_a__U12 => 0 null_a__U21 => 0 null_a__U22 => 0 null_a__U31 => 0 null_a__U32 => 0 null_a__U41 => 0 null_a__U42 => 0 null_a__U43 => 0 null_a__U51 => 0 null_a__U52 => 0 null_a__U53 => 0 null_a__U61 => 0 null_a__U62 => 0 null_a__U63 => 0 null_a__U71 => 0 null_a__U81 => 0 null_a__U91 => 0 null_a__and => 0 null_a__isNat => 0 null_a__isNatIList => 0 null_a__isNatIListKind => 0 null_a__isNatKind => 0 null_a__isNatList => 0 null_a__length => 0 null_a__take => 0 null_mark => 0 null_A__U41 => 0 null_A__U51 => 0 null_A__U61 => 0 null_A__U71 => 0 null_A__U91 => 0 null_A__AND => 0 null_A__ISNAT => 0 null_A__ISNATILISTKIND => 0 null_A__ISNATKIND => 0 null_A__ISNATLIST => 0 null_A__LENGTH => 0 null_A__TAKE => 0 null_MARK => 0 null_A__U11 => 0 null_A__U21 => 0 null_A__U31 => 0 null_A__U42 => 0 null_A__U52 => 0 null_A__U62 => 0 const => 0 ---------------------------------------- (62) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__ISNAT(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__ISNAT(z) -{ 1 }-> 1 + A__U21(a__isNatKind(z0), z0) + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__isNatIListKind(z0), z0) + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U31(a__isNatIListKind(z0), z0) + A__ISNATILISTKIND(z0) :|: z = z0, z0 >= 0 A__ISNATILIST(z) -{ 1 }-> 1 + A__U41(a__and(a__isNatKind(z0), 1 + z1), z0, z1) + A__AND(a__isNatKind(z0), 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATILISTKIND(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__ISNATILISTKIND(z) -{ 1 }-> 1 + A__AND(a__isNatKind(z0), 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATKIND(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATKIND(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0 A__ISNATLIST(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__ISNATLIST(z) -{ 1 }-> 1 + A__U61(a__and(a__isNatKind(z0), 1 + z1), z0, z1) + A__AND(a__isNatKind(z0), 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNATLIST(z) -{ 1 }-> 1 + A__U51(a__and(a__isNatKind(z0), 1 + z1), z0, z1) + A__AND(a__isNatKind(z0), 1 + z1) + A__ISNATKIND(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__LENGTH(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__LENGTH(z) -{ 1 }-> 1 + A__U71(a__and(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) + A__AND(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)) + A__AND(a__isNatList(z1), 1 + z1) + A__ISNATLIST(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__TAKE(z, z') -{ 1 }-> 1 + A__AND(a__isNatIList(z0), 1 + z0) + A__ISNATILIST(z0) :|: z0 >= 0, z = 0, z' = z0 A__TAKE(z, z') -{ 1 }-> 1 + A__U91(a__and(a__and(a__isNatIList(z2), 1 + z2), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))), z2, z0, z1) + A__AND(a__and(a__isNatIList(z2), 1 + z2), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))) + A__AND(a__isNatIList(z2), 1 + z2) + A__ISNATILIST(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U11(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U21(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 2, z0 >= 0, z' = z0 A__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U31(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__isNat(z0), z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U42(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U42(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U51(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__isNat(z0), z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U52(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U52(z, z') -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U61(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U61(z, z', z'') -{ 1 }-> 1 + A__U62(a__isNat(z0), z1) + A__ISNAT(z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 A__U62(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U62(z, z') -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 2, z0 >= 0, z' = z0 A__U71(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U71(z, z') -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 2, z0 >= 0, z' = z0 A__U91(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 A__U91(z, z', z'', z4) -{ 1 }-> 1 + MARK(z2) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATLIST(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATKIND(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATILISTKIND(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNATILIST(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U91(mark(z0), z1, z2, z3) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + A__U71(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U62(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U61(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U52(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U42(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__LENGTH(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__U11(z, z') -{ 0 }-> a__U12(a__isNatList(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U12(z) -{ 0 }-> 2 :|: z = 2 a__U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U12(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U21(z, z') -{ 0 }-> a__U22(a__isNat(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U21(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U21(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U22(z) -{ 0 }-> 2 :|: z = 2 a__U22(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U22(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U31(z, z') -{ 0 }-> a__U32(a__isNatList(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U32(z) -{ 0 }-> 2 :|: z = 2 a__U32(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U32(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U41(z, z', z'') -{ 0 }-> a__U42(a__isNat(z0), z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U41(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U42(z, z') -{ 0 }-> a__U43(a__isNatIList(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U42(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U42(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U43(z) -{ 0 }-> 2 :|: z = 2 a__U43(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U43(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U51(z, z', z'') -{ 0 }-> a__U52(a__isNat(z0), z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U51(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U51(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U52(z, z') -{ 0 }-> a__U53(a__isNatList(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U52(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U52(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U53(z) -{ 0 }-> 2 :|: z = 2 a__U53(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U53(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U61(z, z', z'') -{ 0 }-> a__U62(a__isNat(z0), z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1 a__U61(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U61(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U62(z, z') -{ 0 }-> a__U63(a__isNatIList(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U62(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U62(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U63(z) -{ 0 }-> 2 :|: z = 2 a__U63(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U63(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U71(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U71(z, z') -{ 0 }-> 1 + a__length(mark(z0)) :|: z = 2, z0 >= 0, z' = z0 a__U71(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U81(z) -{ 0 }-> 1 :|: z = 2 a__U81(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U81(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z4 = v3, v2 >= 0, v3 >= 0 a__U91(z, z', z'', z4) -{ 0 }-> 1 + mark(z2) + (1 + z1 + z0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z2 >= 0, z'' = z1, z4 = z2 a__U91(z, z', z'', z4) -{ 0 }-> 1 + z0 + z1 + z2 + z3 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z4 = z3, z2 >= 0, z3 >= 0 a__and(z, z') -{ 0 }-> mark(z0) :|: z = 2, z0 >= 0, z' = z0 a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__isNat(z) -{ 0 }-> a__U21(a__isNatKind(z0), z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__isNatIListKind(z0), z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> 2 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> a__U41(a__and(a__isNatKind(z0), 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIList(z) -{ 0 }-> a__U31(a__isNatIListKind(z0), z0) :|: z = z0, z0 >= 0 a__isNatIList(z) -{ 0 }-> 2 :|: z = 3 a__isNatIList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatIList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatIListKind(z) -{ 0 }-> a__and(a__isNatKind(z0), 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 1 a__isNatIListKind(z) -{ 0 }-> 2 :|: z = 3 a__isNatIListKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatIListKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> a__isNatIListKind(z0) :|: z = 1 + z0, z0 >= 0 a__isNatKind(z) -{ 0 }-> 2 :|: z = 0 a__isNatKind(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatKind(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__isNatList(z) -{ 0 }-> a__U61(a__and(a__isNatKind(z0), 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> a__U51(a__and(a__isNatKind(z0), 1 + z1), z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNatList(z) -{ 0 }-> 2 :|: z = 1 a__isNatList(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNatList(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__length(z) -{ 0 }-> a__U71(a__and(a__and(a__isNatList(z1), 1 + z1), 1 + (1 + z0) + (1 + z0)), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__length(z) -{ 0 }-> 0 :|: z = 1 a__length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__length(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__take(z, z') -{ 0 }-> a__U91(a__and(a__and(a__isNatIList(z2), 1 + z2), 1 + (1 + (1 + z0) + (1 + z0)) + (1 + (1 + z1) + (1 + z1))), z2, z0, z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__take(z, z') -{ 0 }-> a__U81(a__and(a__isNatIList(z0), 1 + z0)) :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__take(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__zeros -{ 0 }-> 3 :|: a__zeros -{ 0 }-> 0 :|: a__zeros -{ 0 }-> 1 + 0 + 3 :|: mark(z) -{ 0 }-> a__zeros :|: z = 3 mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__length(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatList(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatKind(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatIListKind(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNatIList(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__and(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U91(mark(z0), z1, z2, z3) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 + z2 + z3, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__U81(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U71(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U63(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U62(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U61(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U53(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U52(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U51(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U43(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U42(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U41(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U32(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U22(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U21(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U12(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U11(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, z0, z1) -> c14(A__U42(a__isNat(z0), z1), A__ISNAT(z0)) by A__U41(tt, 0, x1) -> c14(A__U42(tt, x1), A__ISNAT(0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, z0, x1) -> c14(A__U42(isNat(z0), x1), A__ISNAT(z0)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1), A__ISNAT(0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, z0, x1) -> c14(A__U42(isNat(z0), x1), A__ISNAT(z0)) S tuples: A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1), A__ISNAT(0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, z0, x1) -> c14(A__U42(isNat(z0), x1), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U51_3, A__U61_3, A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3 Compound Symbols: c20_2, c26_2, c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) S tuples: A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U51_3, A__U61_3, A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3 Compound Symbols: c20_2, c26_2, c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U51(tt, z0, z1) -> c20(A__U52(a__isNat(z0), z1), A__ISNAT(z0)) by A__U51(tt, 0, x1) -> c20(A__U52(tt, x1), A__ISNAT(0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, z0, x1) -> c20(A__U52(isNat(z0), x1), A__ISNAT(z0)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1), A__ISNAT(0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, z0, x1) -> c20(A__U52(isNat(z0), x1), A__ISNAT(z0)) S tuples: A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1), A__ISNAT(0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, z0, x1) -> c20(A__U52(isNat(z0), x1), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U61_3, A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3 Compound Symbols: c26_2, c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) S tuples: A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U61_3, A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3 Compound Symbols: c26_2, c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, z0, z1) -> c26(A__U62(a__isNat(z0), z1), A__ISNAT(z0)) by A__U61(tt, 0, x1) -> c26(A__U62(tt, x1), A__ISNAT(0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, z0, x1) -> c26(A__U62(isNat(z0), x1), A__ISNAT(z0)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1), A__ISNAT(0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, z0, x1) -> c26(A__U62(isNat(z0), x1), A__ISNAT(z0)) S tuples: A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1), A__ISNAT(0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, z0, x1) -> c26(A__U62(isNat(z0), x1), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3 Compound Symbols: c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) S tuples: A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U71_2, A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3 Compound Symbols: c32_2, c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U71(tt, z0) -> c32(A__LENGTH(mark(z0)), MARK(z0)) by A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros), MARK(zeros)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, 0) -> c32(A__LENGTH(0), MARK(0)) A__U71(tt, tt) -> c32(A__LENGTH(tt), MARK(tt)) A__U71(tt, s(z0)) -> c32(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U71(tt, nil) -> c32(A__LENGTH(nil), MARK(nil)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros), MARK(zeros)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, 0) -> c32(A__LENGTH(0), MARK(0)) A__U71(tt, tt) -> c32(A__LENGTH(tt), MARK(tt)) A__U71(tt, s(z0)) -> c32(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U71(tt, nil) -> c32(A__LENGTH(nil), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros), MARK(zeros)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, 0) -> c32(A__LENGTH(0), MARK(0)) A__U71(tt, tt) -> c32(A__LENGTH(tt), MARK(tt)) A__U71(tt, s(z0)) -> c32(A__LENGTH(s(mark(z0))), MARK(s(z0))) A__U71(tt, nil) -> c32(A__LENGTH(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2 Compound Symbols: c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: A__U71(tt, nil) -> c32(A__LENGTH(nil), MARK(nil)) A__U71(tt, tt) -> c32(A__LENGTH(tt), MARK(tt)) A__U71(tt, 0) -> c32(A__LENGTH(0), MARK(0)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros), MARK(zeros)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, s(z0)) -> c32(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros), MARK(zeros)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, s(z0)) -> c32(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2 Compound Symbols: c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2 Compound Symbols: c36_1, c38_1, c41_2, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(length(z0)) -> c41(A__U11(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) by A__ISNAT(length(nil)) -> c41(A__U11(tt, nil), A__ISNATILISTKIND(nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros), A__ISNATILISTKIND(zeros)) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(z0)) -> c41(A__U11(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil), A__ISNATILISTKIND(nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros), A__ISNATILISTKIND(zeros)) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(z0)) -> c41(A__U11(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil), A__ISNATILISTKIND(nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros), A__ISNATILISTKIND(zeros)) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(z0)) -> c41(A__U11(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2 Compound Symbols: c36_1, c38_1, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2 Compound Symbols: c36_1, c38_1, c42_2, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(s(z0)) -> c42(A__U21(a__isNatKind(z0), z0), A__ISNATKIND(z0)) by A__ISNAT(s(0)) -> c42(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c42(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(0)) -> c42(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c42(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(0)) -> c42(A__U21(tt, 0), A__ISNATKIND(0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(z0)) -> c42(A__U21(isNatKind(z0), z0), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1 Compound Symbols: c36_1, c38_1, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1 Compound Symbols: c36_1, c38_1, c44_2, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATILIST(z0) -> c44(A__U31(a__isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) by A__ISNATILIST(nil) -> c44(A__U31(tt, nil), A__ISNATILISTKIND(nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros), A__ISNATILISTKIND(zeros)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(z0) -> c44(A__U31(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(nil) -> c44(A__U31(tt, nil), A__ISNATILISTKIND(nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros), A__ISNATILISTKIND(zeros)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(z0) -> c44(A__U31(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(nil) -> c44(A__U31(tt, nil), A__ISNATILISTKIND(nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros), A__ISNATILISTKIND(zeros)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(z0) -> c44(A__U31(isNatIListKind(z0), z0), A__ISNATILISTKIND(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1 Compound Symbols: c36_1, c38_1, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1 Compound Symbols: c36_1, c38_1, c46_3, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATILIST(cons(z0, z1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) by A__ISNATILIST(cons(x0, x1)) -> c46(A__U41(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__U41(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__U41(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1 Compound Symbols: c36_1, c38_1, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1 Compound Symbols: c36_1, c38_1, c50_2, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATILISTKIND(cons(z0, z1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) by A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__AND(isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__AND(isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__AND(isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1 Compound Symbols: c36_1, c38_1, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATILISTKIND_1, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1 Compound Symbols: c36_1, c38_1, c51_2, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATILISTKIND(take(z0, z1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) by A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__AND(isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__AND(isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__AND(isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c58_3, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATLIST(cons(z0, z1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) by A__ISNATLIST(cons(x0, x1)) -> c58(A__U51(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__U51(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__U51(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c59_3, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNATLIST(take(z0, z1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), A__AND(a__isNatKind(z0), isNatIListKind(z1)), A__ISNATKIND(z0)) by A__ISNATLIST(take(x0, x1)) -> c59(A__U61(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(x0, x1)) -> c59(A__U61(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(x0, x1)) -> c59(A__U61(and(a__isNatKind(x0), isNatIListKind(x1)), x0, x1), A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1)), A__ISNATKIND(0)) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, A__LENGTH_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c62_4, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__LENGTH(cons(z0, z1)) -> c62(A__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1), A__AND(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), A__AND(a__isNatList(z1), isNatIListKind(z1)), A__ISNATLIST(z1)) by A__LENGTH(cons(x0, x1)) -> c62(A__U71(and(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__U71(a__and(a__and(tt, isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), nil), A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)), A__ISNATLIST(nil)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(and(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__U71(a__and(a__and(tt, isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), nil), A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)), A__ISNATLIST(nil)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(and(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__U71(a__and(a__and(tt, isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), nil), A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil)), A__ISNATLIST(nil)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, A__TAKE_2, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c65_4, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__TAKE(s(z0), cons(z1, z2)) -> c65(A__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1), A__AND(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), A__AND(a__isNatIList(z2), isNatIListKind(z2)), A__ISNATILIST(z2)) by A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(and(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(and(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(and(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c68_2, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(z0, z1)) -> c68(A__U11(mark(z0), z1), MARK(z0)) by MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(cons(z0, z1), x1)) -> c68(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(0, x1)) -> c68(A__U11(0, x1), MARK(0)) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c68(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(nil, x1)) -> c68(A__U11(nil, x1), MARK(nil)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(cons(z0, z1), x1)) -> c68(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(0, x1)) -> c68(A__U11(0, x1), MARK(0)) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c68(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(nil, x1)) -> c68(A__U11(nil, x1), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(cons(z0, z1), x1)) -> c68(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(0, x1)) -> c68(A__U11(0, x1), MARK(0)) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c68(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(nil, x1)) -> c68(A__U11(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2 ---------------------------------------- (123) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U11(nil, x1)) -> c68(A__U11(nil, x1), MARK(nil)) MARK(U11(0, x1)) -> c68(A__U11(0, x1), MARK(0)) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(cons(z0, z1), x1)) -> c68(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c68(A__U11(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1), MARK(zeros)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(cons(z0, z1), x1)) -> c68(A__U11(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c68(A__U11(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c71_2, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U21(z0, z1)) -> c71(A__U21(mark(z0), z1), MARK(z0)) by MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1), MARK(zeros)) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(cons(z0, z1), x1)) -> c71(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U21(0, x1)) -> c71(A__U21(0, x1), MARK(0)) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c71(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(nil, x1)) -> c71(A__U21(nil, x1), MARK(nil)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1), MARK(zeros)) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(cons(z0, z1), x1)) -> c71(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U21(0, x1)) -> c71(A__U21(0, x1), MARK(0)) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c71(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(nil, x1)) -> c71(A__U21(nil, x1), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1), MARK(zeros)) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(cons(z0, z1), x1)) -> c71(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U21(0, x1)) -> c71(A__U21(0, x1), MARK(0)) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c71(A__U21(s(mark(z0)), x1), MARK(s(z0))) MARK(U21(nil, x1)) -> c71(A__U21(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2 ---------------------------------------- (129) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U21(nil, x1)) -> c71(A__U21(nil, x1), MARK(nil)) MARK(U21(0, x1)) -> c71(A__U21(0, x1), MARK(0)) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1), MARK(zeros)) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(cons(z0, z1), x1)) -> c71(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c71(A__U21(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1), MARK(zeros)) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(cons(z0, z1), x1)) -> c71(A__U21(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1), MARK(tt)) MARK(U21(s(z0), x1)) -> c71(A__U21(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c74_2, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U31(z0, z1)) -> c74(A__U31(mark(z0), z1), MARK(z0)) by MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1), MARK(zeros)) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(cons(z0, z1), x1)) -> c74(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U31(0, x1)) -> c74(A__U31(0, x1), MARK(0)) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c74(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(nil, x1)) -> c74(A__U31(nil, x1), MARK(nil)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1), MARK(zeros)) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(cons(z0, z1), x1)) -> c74(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U31(0, x1)) -> c74(A__U31(0, x1), MARK(0)) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c74(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(nil, x1)) -> c74(A__U31(nil, x1), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1), MARK(zeros)) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(cons(z0, z1), x1)) -> c74(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U31(0, x1)) -> c74(A__U31(0, x1), MARK(0)) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c74(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(nil, x1)) -> c74(A__U31(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2 ---------------------------------------- (135) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U31(0, x1)) -> c74(A__U31(0, x1), MARK(0)) MARK(U31(nil, x1)) -> c74(A__U31(nil, x1), MARK(nil)) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1), MARK(zeros)) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(cons(z0, z1), x1)) -> c74(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c74(A__U31(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1), MARK(zeros)) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(cons(z0, z1), x1)) -> c74(A__U31(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c74(A__U31(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c76_2, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1 ---------------------------------------- (139) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U41(z0, z1, z2)) -> c76(A__U41(mark(z0), z1, z2), MARK(z0)) by MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2), MARK(zeros)) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(cons(z0, z1), x1, x2)) -> c76(A__U41(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U41(0, x1, x2)) -> c76(A__U41(0, x1, x2), MARK(0)) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c76(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(nil, x1, x2)) -> c76(A__U41(nil, x1, x2), MARK(nil)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2), MARK(zeros)) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(cons(z0, z1), x1, x2)) -> c76(A__U41(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U41(0, x1, x2)) -> c76(A__U41(0, x1, x2), MARK(0)) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c76(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(nil, x1, x2)) -> c76(A__U41(nil, x1, x2), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2), MARK(zeros)) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(cons(z0, z1), x1, x2)) -> c76(A__U41(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U41(0, x1, x2)) -> c76(A__U41(0, x1, x2), MARK(0)) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c76(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U41(nil, x1, x2)) -> c76(A__U41(nil, x1, x2), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2 ---------------------------------------- (141) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U41(0, x1, x2)) -> c76(A__U41(0, x1, x2), MARK(0)) MARK(U41(nil, x1, x2)) -> c76(A__U41(nil, x1, x2), MARK(nil)) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2), MARK(zeros)) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(cons(z0, z1), x1, x2)) -> c76(A__U41(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c76(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2), MARK(zeros)) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(cons(z0, z1), x1, x2)) -> c76(A__U41(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2), MARK(tt)) MARK(U41(s(z0), x1, x2)) -> c76(A__U41(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c77_2, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U42(z0, z1)) -> c77(A__U42(mark(z0), z1), MARK(z0)) by MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1), MARK(zeros)) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(cons(z0, z1), x1)) -> c77(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U42(0, x1)) -> c77(A__U42(0, x1), MARK(0)) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1), MARK(tt)) MARK(U42(s(z0), x1)) -> c77(A__U42(s(mark(z0)), x1), MARK(s(z0))) MARK(U42(nil, x1)) -> c77(A__U42(nil, x1), MARK(nil)) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1), MARK(zeros)) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(cons(z0, z1), x1)) -> c77(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U42(0, x1)) -> c77(A__U42(0, x1), MARK(0)) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1), MARK(tt)) MARK(U42(s(z0), x1)) -> c77(A__U42(s(mark(z0)), x1), MARK(s(z0))) MARK(U42(nil, x1)) -> c77(A__U42(nil, x1), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1), MARK(zeros)) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(cons(z0, z1), x1)) -> c77(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U42(0, x1)) -> c77(A__U42(0, x1), MARK(0)) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1), MARK(tt)) MARK(U42(s(z0), x1)) -> c77(A__U42(s(mark(z0)), x1), MARK(s(z0))) MARK(U42(nil, x1)) -> c77(A__U42(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2 ---------------------------------------- (147) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U42(nil, x1)) -> c77(A__U42(nil, x1), MARK(nil)) MARK(U42(0, x1)) -> c77(A__U42(0, x1), MARK(0)) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1), MARK(zeros)) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(cons(z0, z1), x1)) -> c77(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1), MARK(tt)) MARK(U42(s(z0), x1)) -> c77(A__U42(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1), MARK(zeros)) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(cons(z0, z1), x1)) -> c77(A__U42(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1), MARK(tt)) MARK(U42(s(z0), x1)) -> c77(A__U42(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2 ---------------------------------------- (149) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c80_2, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U51(z0, z1, z2)) -> c80(A__U51(mark(z0), z1, z2), MARK(z0)) by MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2), MARK(zeros)) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(cons(z0, z1), x1, x2)) -> c80(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U51(0, x1, x2)) -> c80(A__U51(0, x1, x2), MARK(0)) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c80(A__U51(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U51(nil, x1, x2)) -> c80(A__U51(nil, x1, x2), MARK(nil)) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2), MARK(zeros)) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(cons(z0, z1), x1, x2)) -> c80(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U51(0, x1, x2)) -> c80(A__U51(0, x1, x2), MARK(0)) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c80(A__U51(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U51(nil, x1, x2)) -> c80(A__U51(nil, x1, x2), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2), MARK(zeros)) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(cons(z0, z1), x1, x2)) -> c80(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U51(0, x1, x2)) -> c80(A__U51(0, x1, x2), MARK(0)) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c80(A__U51(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U51(nil, x1, x2)) -> c80(A__U51(nil, x1, x2), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2 ---------------------------------------- (153) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U51(nil, x1, x2)) -> c80(A__U51(nil, x1, x2), MARK(nil)) MARK(U51(0, x1, x2)) -> c80(A__U51(0, x1, x2), MARK(0)) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2), MARK(zeros)) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(cons(z0, z1), x1, x2)) -> c80(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c80(A__U51(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2), MARK(zeros)) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(cons(z0, z1), x1, x2)) -> c80(A__U51(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c80(A__U51(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c81_2, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U52(z0, z1)) -> c81(A__U52(mark(z0), z1), MARK(z0)) by MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1), MARK(zeros)) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(cons(z0, z1), x1)) -> c81(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U52(0, x1)) -> c81(A__U52(0, x1), MARK(0)) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c81(A__U52(s(mark(z0)), x1), MARK(s(z0))) MARK(U52(nil, x1)) -> c81(A__U52(nil, x1), MARK(nil)) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1), MARK(zeros)) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(cons(z0, z1), x1)) -> c81(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U52(0, x1)) -> c81(A__U52(0, x1), MARK(0)) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c81(A__U52(s(mark(z0)), x1), MARK(s(z0))) MARK(U52(nil, x1)) -> c81(A__U52(nil, x1), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1), MARK(zeros)) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(cons(z0, z1), x1)) -> c81(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U52(0, x1)) -> c81(A__U52(0, x1), MARK(0)) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c81(A__U52(s(mark(z0)), x1), MARK(s(z0))) MARK(U52(nil, x1)) -> c81(A__U52(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2 ---------------------------------------- (159) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U52(0, x1)) -> c81(A__U52(0, x1), MARK(0)) MARK(U52(nil, x1)) -> c81(A__U52(nil, x1), MARK(nil)) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1), MARK(zeros)) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(cons(z0, z1), x1)) -> c81(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c81(A__U52(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1), MARK(zeros)) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(cons(z0, z1), x1)) -> c81(A__U52(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1), MARK(tt)) MARK(U52(s(z0), x1)) -> c81(A__U52(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2 ---------------------------------------- (161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c83_2, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1 ---------------------------------------- (163) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U61(z0, z1, z2)) -> c83(A__U61(mark(z0), z1, z2), MARK(z0)) by MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2), MARK(zeros)) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(cons(z0, z1), x1, x2)) -> c83(A__U61(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U61(0, x1, x2)) -> c83(A__U61(0, x1, x2), MARK(0)) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2), MARK(tt)) MARK(U61(s(z0), x1, x2)) -> c83(A__U61(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U61(nil, x1, x2)) -> c83(A__U61(nil, x1, x2), MARK(nil)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2), MARK(zeros)) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(cons(z0, z1), x1, x2)) -> c83(A__U61(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U61(0, x1, x2)) -> c83(A__U61(0, x1, x2), MARK(0)) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2), MARK(tt)) MARK(U61(s(z0), x1, x2)) -> c83(A__U61(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U61(nil, x1, x2)) -> c83(A__U61(nil, x1, x2), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), 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MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2), MARK(zeros)) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(cons(z0, z1), x1, x2)) -> c83(A__U61(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U61(0, x1, x2)) -> c83(A__U61(0, x1, x2), MARK(0)) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2), MARK(tt)) MARK(U61(s(z0), x1, x2)) -> c83(A__U61(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U61(nil, x1, x2)) -> c83(A__U61(nil, x1, x2), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2 ---------------------------------------- (165) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U61(nil, x1, x2)) -> c83(A__U61(nil, x1, x2), MARK(nil)) MARK(U61(0, x1, x2)) -> c83(A__U61(0, x1, x2), MARK(0)) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> 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MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2), MARK(zeros)) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(cons(z0, z1), x1, x2)) -> c83(A__U61(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2), MARK(tt)) MARK(U61(s(z0), x1, x2)) -> c83(A__U61(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> 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MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, 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MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2), MARK(zeros)) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(cons(z0, z1), x1, x2)) -> c83(A__U61(cons(mark(z0), z1), x1, x2), MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2), MARK(tt)) MARK(U61(s(z0), x1, x2)) -> c83(A__U61(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) 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MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), 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MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c84_2, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U62(z0, z1)) -> c84(A__U62(mark(z0), z1), MARK(z0)) by MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1), MARK(zeros)) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(cons(z0, z1), x1)) -> c84(A__U62(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U62(0, x1)) -> c84(A__U62(0, x1), MARK(0)) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1), MARK(tt)) MARK(U62(s(z0), x1)) -> c84(A__U62(s(mark(z0)), x1), MARK(s(z0))) MARK(U62(nil, x1)) -> c84(A__U62(nil, x1), MARK(nil)) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> 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c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1), MARK(zeros)) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(cons(z0, z1), x1)) -> c84(A__U62(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U62(0, x1)) -> c84(A__U62(0, x1), MARK(0)) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1), MARK(tt)) MARK(U62(s(z0), x1)) -> c84(A__U62(s(mark(z0)), x1), MARK(s(z0))) MARK(U62(nil, x1)) -> c84(A__U62(nil, x1), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> 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MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, 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MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1), MARK(zeros)) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(cons(z0, z1), x1)) -> c84(A__U62(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U62(0, x1)) -> c84(A__U62(0, x1), MARK(0)) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1), MARK(tt)) MARK(U62(s(z0), x1)) -> c84(A__U62(s(mark(z0)), x1), MARK(s(z0))) MARK(U62(nil, x1)) -> c84(A__U62(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2 ---------------------------------------- (171) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U62(0, x1)) -> c84(A__U62(0, x1), MARK(0)) MARK(U62(nil, x1)) -> c84(A__U62(nil, x1), MARK(nil)) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1), MARK(zeros)) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(cons(z0, z1), x1)) -> c84(A__U62(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1), MARK(tt)) MARK(U62(s(z0), x1)) -> c84(A__U62(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1), MARK(zeros)) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(cons(z0, z1), x1)) -> c84(A__U62(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1), MARK(tt)) MARK(U62(s(z0), x1)) -> c84(A__U62(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2 ---------------------------------------- (173) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), 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x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c86_2, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1 ---------------------------------------- (175) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U71(z0, z1)) -> c86(A__U71(mark(z0), z1), MARK(z0)) by MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1), MARK(zeros)) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(cons(z0, z1), x1)) -> c86(A__U71(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U71(0, x1)) -> c86(A__U71(0, x1), MARK(0)) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1), MARK(tt)) MARK(U71(s(z0), x1)) -> c86(A__U71(s(mark(z0)), x1), MARK(s(z0))) MARK(U71(nil, x1)) -> c86(A__U71(nil, x1), MARK(nil)) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), 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c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1), MARK(zeros)) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(cons(z0, z1), x1)) -> c86(A__U71(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U71(0, x1)) -> c86(A__U71(0, x1), MARK(0)) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1), MARK(tt)) MARK(U71(s(z0), x1)) -> c86(A__U71(s(mark(z0)), x1), MARK(s(z0))) MARK(U71(nil, x1)) -> c86(A__U71(nil, x1), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) 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MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(cons(z0, z1), x1)) -> c86(A__U71(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U71(0, x1)) -> c86(A__U71(0, x1), MARK(0)) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1), MARK(tt)) MARK(U71(s(z0), x1)) -> c86(A__U71(s(mark(z0)), x1), MARK(s(z0))) MARK(U71(nil, x1)) -> c86(A__U71(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2 ---------------------------------------- (177) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U71(nil, x1)) -> c86(A__U71(nil, x1), MARK(nil)) MARK(U71(0, x1)) -> c86(A__U71(0, x1), MARK(0)) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1), MARK(zeros)) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(cons(z0, z1), x1)) -> c86(A__U71(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1), MARK(tt)) MARK(U71(s(z0), x1)) -> c86(A__U71(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1), MARK(zeros)) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(cons(z0, z1), x1)) -> c86(A__U71(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1), MARK(tt)) MARK(U71(s(z0), x1)) -> c86(A__U71(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c87_2, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1 ---------------------------------------- (181) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(length(z0)) -> c87(A__LENGTH(mark(z0)), MARK(z0)) by MARK(length(zeros)) -> c87(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c87(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c87(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c87(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c87(A__LENGTH(nil), MARK(nil)) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c87(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c87(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c87(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c87(A__LENGTH(nil), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(0)) -> c87(A__LENGTH(0), MARK(0)) MARK(length(tt)) -> c87(A__LENGTH(tt), MARK(tt)) MARK(length(s(z0))) -> c87(A__LENGTH(s(mark(z0))), MARK(s(z0))) MARK(length(nil)) -> c87(A__LENGTH(nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2 ---------------------------------------- (183) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(length(tt)) -> c87(A__LENGTH(tt), MARK(tt)) MARK(length(nil)) -> c87(A__LENGTH(nil), MARK(nil)) MARK(length(0)) -> c87(A__LENGTH(0), MARK(0)) ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c87(A__LENGTH(s(mark(z0))), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros), MARK(zeros)) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(s(z0))) -> c87(A__LENGTH(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2 ---------------------------------------- (185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c89_2, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1 ---------------------------------------- (187) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U91(z0, z1, z2, z3)) -> c89(A__U91(mark(z0), z1, z2, z3), MARK(z0)) by MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U91(0, x1, x2, x3)) -> c89(A__U91(0, x1, x2, x3), MARK(0)) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3), MARK(tt)) MARK(U91(s(z0), x1, x2, x3)) -> c89(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U91(nil, x1, x2, x3)) -> c89(A__U91(nil, x1, x2, x3), MARK(nil)) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) 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MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U91(0, x1, x2, x3)) -> c89(A__U91(0, x1, x2, x3), MARK(0)) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3), MARK(tt)) MARK(U91(s(z0), x1, x2, x3)) -> c89(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U91(nil, x1, x2, x3)) -> c89(A__U91(nil, x1, x2, x3), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> 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x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U91(0, x1, x2, x3)) -> c89(A__U91(0, x1, x2, x3), MARK(0)) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3), MARK(tt)) MARK(U91(s(z0), x1, x2, x3)) -> c89(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0))) MARK(U91(nil, x1, x2, x3)) -> c89(A__U91(nil, x1, x2, x3), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2 ---------------------------------------- (189) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(U91(nil, x1, x2, x3)) -> c89(A__U91(nil, x1, x2, x3), MARK(nil)) MARK(U91(0, x1, x2, x3)) -> c89(A__U91(0, x1, x2, x3), MARK(0)) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3), MARK(tt)) MARK(U91(s(z0), x1, x2, x3)) -> c89(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) 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MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3), MARK(zeros)) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(A__U91(cons(mark(z0), z1), x1, x2, x3), MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3), MARK(tt)) MARK(U91(s(z0), x1, x2, x3)) -> c89(A__U91(s(mark(z0)), x1, x2, x3), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> 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MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, 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c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c90_2, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1 ---------------------------------------- (193) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c90(A__TAKE(mark(z0), mark(z1)), MARK(z0)) by MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(cons(z0, z1), x1)) -> c90(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c90(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c90(A__TAKE(nil, mark(x1)), MARK(nil)) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, 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MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> 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x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(cons(z0, z1), x1)) -> c90(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c90(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c90(A__TAKE(nil, mark(x1)), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(cons(z0, z1), x1)) -> c90(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(tt, x1)) -> c90(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c90(A__TAKE(nil, mark(x1)), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2 ---------------------------------------- (195) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(tt, x1)) -> c90(A__TAKE(tt, mark(x1)), MARK(tt)) MARK(take(nil, x1)) -> c90(A__TAKE(nil, mark(x1)), MARK(nil)) ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) 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MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, 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MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(cons(z0, z1), x1)) -> c90(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1)), MARK(zeros)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(cons(z0, z1), x1)) -> c90(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2 ---------------------------------------- (197) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), 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c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c91_2, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1 ---------------------------------------- (199) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c91(A__TAKE(mark(z0), mark(z1)), MARK(z1)) by MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c91(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c91(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c91(A__TAKE(nil, mark(x1)), MARK(x1)) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> 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isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros), MARK(zeros)) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c91(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c91(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c91(A__TAKE(nil, mark(x1)), MARK(x1)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> 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z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt), MARK(tt)) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c91(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(tt, x1)) -> c91(A__TAKE(tt, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c91(A__TAKE(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) 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x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c92_2, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1 ---------------------------------------- (203) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(z0, z1)) -> c92(A__AND(mark(z0), z1), MARK(z0)) by MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(cons(z0, z1), x1)) -> c92(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c92(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c92(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c92(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(nil, x1)) -> c92(A__AND(nil, x1), MARK(nil)) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), 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z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> 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x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(cons(z0, z1), x1)) -> c92(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c92(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c92(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c92(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(nil, x1)) -> c92(A__AND(nil, x1), MARK(nil)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), 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z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(cons(z0, z1), x1)) -> c92(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(0, x1)) -> c92(A__AND(0, x1), MARK(0)) MARK(and(tt, x1)) -> c92(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c92(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(nil, x1)) -> c92(A__AND(nil, x1), MARK(nil)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2 ---------------------------------------- (205) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(and(0, x1)) -> c92(A__AND(0, x1), MARK(0)) MARK(and(nil, x1)) -> c92(A__AND(nil, x1), MARK(nil)) ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, 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MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) 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MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), 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c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(cons(z0, z1), x1)) -> c92(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c92(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) 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c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), 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mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1), MARK(zeros)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(cons(z0, z1), x1)) -> c92(A__AND(cons(mark(z0), z1), x1), MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c92(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2 ---------------------------------------- (207) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, 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c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__TAKE_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c64_2, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1 ---------------------------------------- (209) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__TAKE(0, z0) -> c64(A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) by A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__AND(isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), 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MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__AND(isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> 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a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__AND(isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2 ---------------------------------------- (211) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> 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MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), 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z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, 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c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1 ---------------------------------------- (213) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) by A__U41(tt, length(z1), x1) -> c14(A__U42(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1))) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> 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z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(z1), x1) -> c14(A__U42(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1))) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), 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MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), 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x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> 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MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) 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c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(z1), x1) -> c14(A__U42(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1))) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1 ---------------------------------------- (215) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> 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MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, 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MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> 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MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), 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c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> 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MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, 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MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) 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MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_2, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1 ---------------------------------------- (217) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) by A__U41(tt, s(z1), x1) -> c14(A__U42(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> 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z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), 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c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(z1), x1) -> c14(A__U42(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) 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c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(z1), x1) -> c14(A__U42(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2 ---------------------------------------- (219) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), 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c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, 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z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2 ---------------------------------------- (221) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) by A__U51(tt, length(z1), x1) -> c20(A__U52(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) 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z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(z1), x1) -> c20(A__U52(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), 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MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, 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MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), 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MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> 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c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(z1), x1) -> c20(A__U52(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2 ---------------------------------------- (223) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, 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z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> 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MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> 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c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_2, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2 ---------------------------------------- (225) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) by A__U51(tt, s(z1), x1) -> c20(A__U52(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, 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c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(z1), x1) -> c20(A__U52(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, 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c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(z1), x1) -> c20(A__U52(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2 ---------------------------------------- (227) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (228) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, 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c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, 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c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, 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mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> 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z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2 ---------------------------------------- (229) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(a__isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) by A__U61(tt, length(z1), x1) -> c26(A__U62(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, 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z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(z1), x1) -> c26(A__U62(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) 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x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(z1), x1) -> c26(A__U62(U11(a__isNatIListKind(z1), z1), x1), A__ISNAT(length(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2 ---------------------------------------- (231) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (232) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), 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c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, 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c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_2, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2 ---------------------------------------- (233) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), z0), x1), A__ISNAT(s(z0))) by A__U61(tt, s(z1), x1) -> c26(A__U62(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) ---------------------------------------- (234) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> 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MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), 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MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, 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a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1))) A__U61(tt, s(z1), x1) -> c26(A__U62(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> 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a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1))) A__U61(tt, s(z1), x1) -> c26(A__U62(U21(a__isNatKind(z1), z1), x1), A__ISNAT(s(z1))) A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2 ---------------------------------------- (235) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (236) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1))) A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) 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z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1))) A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2 ---------------------------------------- (237) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U71(tt, U11(z0, z1)) -> c32(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) by A__U71(tt, U11(x0, z1)) -> c32(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1))) A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1))) A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1))) A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1))) A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1))) A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1))) A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) ---------------------------------------- (238) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> c90(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(length(z0))) MARK(take(U81(z0), x1)) -> c90(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(U81(z0))) MARK(take(U91(z0, z1, z2, z3), x1)) -> c90(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(U91(z0, z1, z2, z3))) MARK(take(take(z0, z1), x1)) -> c90(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(and(z0, z1), x1)) -> c90(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(take(isNatIListKind(z0), x1)) -> c90(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(isNatIListKind(z0))) MARK(take(isNatKind(z0), x1)) -> c90(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(isNatKind(z0))) MARK(take(s(z0), x1)) -> c90(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(zeros, x1)) -> c90(A__TAKE(a__zeros, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c90(MARK(cons(z0, z1))) MARK(take(0, x1)) -> c90(A__TAKE(0, mark(x1))) MARK(take(x0, U11(z0, z1))) -> c91(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(take(x0, U12(z0))) -> c91(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(take(x0, isNatList(z0))) -> c91(A__TAKE(mark(x0), a__isNatList(z0)), MARK(isNatList(z0))) MARK(take(x0, U21(z0, z1))) -> c91(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(take(x0, U22(z0))) -> c91(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(U22(z0))) MARK(take(x0, isNat(z0))) -> c91(A__TAKE(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(take(x0, U31(z0, z1))) -> c91(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(take(x0, U32(z0))) -> c91(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(take(x0, U41(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(take(x0, U42(z0, z1))) -> c91(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(take(x0, U43(z0))) -> c91(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(U43(z0))) MARK(take(x0, isNatIList(z0))) -> c91(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(take(x0, U51(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(take(x0, U52(z0, z1))) -> c91(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(take(x0, U53(z0))) -> c91(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(U53(z0))) MARK(take(x0, U61(z0, z1, z2))) -> c91(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(take(x0, U62(z0, z1))) -> c91(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(take(x0, U63(z0))) -> c91(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(U63(z0))) MARK(take(x0, U71(z0, z1))) -> c91(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(take(x0, length(z0))) -> c91(A__TAKE(mark(x0), a__length(mark(z0))), MARK(length(z0))) MARK(take(x0, U81(z0))) -> c91(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(U81(z0))) MARK(take(x0, U91(z0, z1, z2, z3))) -> c91(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(take(x0, take(z0, z1))) -> c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1))) A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1))) A__U71(tt, U11(x0, z1)) -> c32(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1))) A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1))) A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1))) A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1))) A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1))) A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1))) A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), 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c91(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, and(z0, z1))) -> c91(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(take(x0, isNatIListKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(take(x0, isNatKind(z0))) -> c91(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(take(x0, cons(z0, z1))) -> c91(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c91(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(zeros, x1)) -> c91(A__TAKE(a__zeros, mark(x1)), MARK(x1)) MARK(take(U11(z0, z1), x1)) -> c91(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U12(z0), x1)) -> c91(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatList(z0), x1)) -> c91(A__TAKE(a__isNatList(z0), mark(x1)), MARK(x1)) MARK(take(U21(z0, z1), x1)) -> c91(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U22(z0), x1)) -> c91(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNat(z0), x1)) -> c91(A__TAKE(a__isNat(z0), mark(x1)), MARK(x1)) MARK(take(U31(z0, z1), x1)) -> c91(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U32(z0), x1)) -> c91(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U41(z0, z1, z2), x1)) -> c91(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U42(z0, z1), x1)) -> c91(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U43(z0), x1)) -> c91(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(x1)) MARK(take(isNatIList(z0), x1)) -> c91(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(x1)) MARK(take(U51(z0, z1, z2), x1)) -> c91(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U52(z0, z1), x1)) -> c91(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U53(z0), x1)) -> c91(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U61(z0, z1, z2), x1)) -> c91(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(take(U62(z0, z1), x1)) -> c91(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(U63(z0), x1)) -> c91(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U71(z0, z1), x1)) -> c91(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(length(z0), x1)) -> c91(A__TAKE(a__length(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U81(z0), x1)) -> c91(A__TAKE(a__U81(mark(z0)), mark(x1)), MARK(x1)) MARK(take(U91(z0, z1, z2, z3), x1)) -> c91(A__TAKE(a__U91(mark(z0), z1, z2, z3), mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c91(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(and(z0, z1), x1)) -> c91(A__TAKE(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(isNatIListKind(z0), x1)) -> c91(A__TAKE(a__isNatIListKind(z0), mark(x1)), MARK(x1)) MARK(take(isNatKind(z0), x1)) -> c91(A__TAKE(a__isNatKind(z0), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c91(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1))) A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1))) A__U71(tt, U11(x0, z1)) -> c32(A__LENGTH(U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1))) A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1))) A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1))) A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1))) A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1))) A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1))) A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1)), MARK(U11(0, x1))) A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1)), MARK(U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2 ---------------------------------------- (239) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (240) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) 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MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, 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MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), 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c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1))) A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1))) A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1))) A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1))) A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1))) A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1))) A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1))) A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1))) A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1))) A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1))) A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, 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c91(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, zeros)) -> c91(A__TAKE(mark(x0), a__zeros)) MARK(take(x0, 0)) -> c91(A__TAKE(mark(x0), 0)) MARK(take(x0, tt)) -> c91(A__TAKE(mark(x0), tt)) MARK(take(x0, nil)) -> c91(A__TAKE(mark(x0), nil)) MARK(take(cons(z0, z1), x1)) -> c91(MARK(x1)) MARK(take(tt, x1)) -> c91(MARK(x1)) MARK(take(nil, x1)) -> c91(MARK(x1)) MARK(and(U11(z0, z1), x1)) -> c92(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U12(z0), x1)) -> c92(A__AND(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(and(isNatList(z0), x1)) -> c92(A__AND(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1))) A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1))) A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1))) A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1))) A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1))) A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1))) A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1))) A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1))) A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1))) A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1))) A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2 ---------------------------------------- (241) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U71(tt, U12(z0)) -> c32(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) by A__U71(tt, U12(x0)) -> c32(A__LENGTH(U12(mark(x0))), MARK(U12(x0))) A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2)))) A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1)))) A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0)))) A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1)))) A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0)))) A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3)))) A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1)))) A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U71(tt, U12(x0)) -> c32(MARK(U12(x0))) ---------------------------------------- (242) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), 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MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1))) A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1))) A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1))) A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1))) A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1))) A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1))) A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1))) A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1))) A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1))) A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1))) A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1))) A__U71(tt, U12(x0)) -> c32(A__LENGTH(U12(mark(x0))), MARK(U12(x0))) A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2)))) A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1)))) A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0)))) A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1)))) A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0)))) A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3)))) A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1)))) A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U71(tt, U12(x0)) -> c32(MARK(U12(x0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> 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c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1))) A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1))) A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1))) A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1))) A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1))) A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1))) A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1))) A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1))) A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1))) A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1))) A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1))) A__U71(tt, U12(x0)) -> c32(A__LENGTH(U12(mark(x0))), MARK(U12(x0))) A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2)))) A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1)))) A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0)))) A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1)))) A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0)))) A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3)))) A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1)))) A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U71(tt, U12(x0)) -> c32(MARK(U12(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2 ---------------------------------------- (243) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (244) Obligation: Complexity Dependency Tuples Problem Rules: a__zeros -> cons(0, zeros) a__zeros -> zeros a__U11(tt, z0) -> a__U12(a__isNatList(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt, z0) -> a__U22(a__isNat(z0)) a__U21(z0, z1) -> U21(z0, z1) a__U22(tt) -> tt a__U22(z0) -> U22(z0) a__U31(tt, z0) -> a__U32(a__isNatList(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0, z1) -> a__U42(a__isNat(z0), z1) a__U41(z0, z1, z2) -> U41(z0, z1, z2) a__U42(tt, z0) -> a__U43(a__isNatIList(z0)) a__U42(z0, z1) -> U42(z0, z1) a__U43(tt) -> tt a__U43(z0) -> U43(z0) a__U51(tt, z0, z1) -> a__U52(a__isNat(z0), z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0) -> a__U53(a__isNatList(z0)) a__U52(z0, z1) -> U52(z0, z1) a__U53(tt) -> tt a__U53(z0) -> U53(z0) a__U61(tt, z0, z1) -> a__U62(a__isNat(z0), z1) a__U61(z0, z1, z2) -> U61(z0, z1, z2) a__U62(tt, z0) -> a__U63(a__isNatIList(z0)) a__U62(z0, z1) -> U62(z0, z1) a__U63(tt) -> tt a__U63(z0) -> U63(z0) a__U71(tt, z0) -> s(a__length(mark(z0))) a__U71(z0, z1) -> U71(z0, z1) a__U81(tt) -> nil a__U81(z0) -> U81(z0) a__U91(tt, z0, z1, z2) -> cons(mark(z2), take(z1, z0)) a__U91(z0, z1, z2, z3) -> U91(z0, z1, z2, z3) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__isNat(0) -> tt a__isNat(length(z0)) -> a__U11(a__isNatIListKind(z0), z0) a__isNat(s(z0)) -> a__U21(a__isNatKind(z0), z0) a__isNat(z0) -> isNat(z0) a__isNatIList(z0) -> a__U31(a__isNatIListKind(z0), z0) a__isNatIList(zeros) -> tt a__isNatIList(cons(z0, z1)) -> a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatIList(z0) -> isNatIList(z0) a__isNatIListKind(nil) -> tt a__isNatIListKind(zeros) -> tt a__isNatIListKind(cons(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(take(z0, z1)) -> a__and(a__isNatKind(z0), isNatIListKind(z1)) a__isNatIListKind(z0) -> isNatIListKind(z0) a__isNatKind(0) -> tt a__isNatKind(length(z0)) -> a__isNatIListKind(z0) a__isNatKind(s(z0)) -> a__isNatKind(z0) a__isNatKind(z0) -> isNatKind(z0) a__isNatList(nil) -> tt a__isNatList(cons(z0, z1)) -> a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(take(z0, z1)) -> a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1) a__isNatList(z0) -> isNatList(z0) a__length(nil) -> 0 a__length(cons(z0, z1)) -> a__U71(a__and(a__and(a__isNatList(z1), isNatIListKind(z1)), and(isNat(z0), isNatKind(z0))), z1) a__length(z0) -> length(z0) a__take(0, z0) -> a__U81(a__and(a__isNatIList(z0), isNatIListKind(z0))) a__take(s(z0), cons(z1, z2)) -> a__U91(a__and(a__and(a__isNatIList(z2), isNatIListKind(z2)), and(and(isNat(z0), isNatKind(z0)), and(isNat(z1), isNatKind(z1)))), z2, z0, z1) a__take(z0, z1) -> take(z0, z1) mark(zeros) -> a__zeros mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNatList(z0)) -> a__isNatList(z0) mark(U21(z0, z1)) -> a__U21(mark(z0), z1) mark(U22(z0)) -> a__U22(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) mark(U42(z0, z1)) -> a__U42(mark(z0), z1) mark(U43(z0)) -> a__U43(mark(z0)) mark(isNatIList(z0)) -> a__isNatIList(z0) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1)) -> a__U52(mark(z0), z1) mark(U53(z0)) -> a__U53(mark(z0)) mark(U61(z0, z1, z2)) -> a__U61(mark(z0), z1, z2) mark(U62(z0, z1)) -> a__U62(mark(z0), z1) mark(U63(z0)) -> a__U63(mark(z0)) mark(U71(z0, z1)) -> a__U71(mark(z0), z1) mark(length(z0)) -> a__length(mark(z0)) mark(U81(z0)) -> a__U81(mark(z0)) mark(U91(z0, z1, z2, z3)) -> a__U91(mark(z0), z1, z2, z3) mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNatIListKind(z0)) -> a__isNatIListKind(z0) mark(isNatKind(z0)) -> a__isNatKind(z0) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil Tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), 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MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, 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MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), 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MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> 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MARK(and(U21(z0, z1), x1)) -> c92(A__AND(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(and(U22(z0), x1)) -> c92(A__AND(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(and(isNat(z0), x1)) -> c92(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(U31(z0, z1), x1)) -> c92(A__AND(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(and(U32(z0), x1)) -> c92(A__AND(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(and(U41(z0, z1, z2), x1)) -> c92(A__AND(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(and(U42(z0, z1), x1)) -> c92(A__AND(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(and(U43(z0), x1)) -> c92(A__AND(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(and(isNatIList(z0), x1)) -> c92(A__AND(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(and(U51(z0, z1, z2), x1)) -> c92(A__AND(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(and(U52(z0, z1), x1)) -> c92(A__AND(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(and(U53(z0), x1)) -> c92(A__AND(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(and(U61(z0, z1, z2), x1)) -> c92(A__AND(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(and(U62(z0, z1), x1)) -> c92(A__AND(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(and(U63(z0), x1)) -> c92(A__AND(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(and(U71(z0, z1), x1)) -> c92(A__AND(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(and(length(z0), x1)) -> c92(A__AND(a__length(mark(z0)), x1), MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1))) A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1))) A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1))) A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1))) A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1))) A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1))) A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1))) A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1))) A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1))) A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1))) A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1))) A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2)))) A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1)))) A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0)))) A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1)))) A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0)))) A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3)))) A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1)))) A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U71(tt, U12(x0)) -> c32(MARK(U12(x0))) S tuples: A__U91(tt, z0, z1, z2) -> c36(MARK(z2)) A__AND(tt, z0) -> c38(MARK(z0)) A__ISNATKIND(length(z0)) -> c54(A__ISNATILISTKIND(z0)) A__ISNATKIND(s(z0)) -> c55(A__ISNATKIND(z0)) MARK(isNatList(z0)) -> c70(A__ISNATLIST(z0)) MARK(isNat(z0)) -> c73(A__ISNAT(z0)) MARK(isNatIList(z0)) -> c79(A__ISNATILIST(z0)) MARK(isNatIListKind(z0)) -> c93(A__ISNATILISTKIND(z0)) MARK(isNatKind(z0)) -> c94(A__ISNATKIND(z0)) MARK(cons(z0, z1)) -> c95(MARK(z0)) MARK(s(z0)) -> c98(MARK(z0)) A__U11(tt, z0) -> c2(A__ISNATLIST(z0)) A__U21(tt, z0) -> c6(A__ISNAT(z0)) A__U31(tt, z0) -> c10(A__ISNATLIST(z0)) A__U42(tt, z0) -> c16(A__ISNATILIST(z0)) A__U52(tt, z0) -> c22(A__ISNATLIST(z0)) A__U62(tt, z0) -> c28(A__ISNATILIST(z0)) MARK(U12(z0)) -> c69(MARK(z0)) MARK(U22(z0)) -> c72(MARK(z0)) MARK(U32(z0)) -> c75(MARK(z0)) MARK(U43(z0)) -> c78(MARK(z0)) MARK(U53(z0)) -> c82(MARK(z0)) MARK(U63(z0)) -> c85(MARK(z0)) MARK(U81(z0)) -> c88(MARK(z0)) A__U41(tt, 0, x1) -> c14(A__U42(tt, x1)) A__U41(tt, z0, x1) -> c14(A__ISNAT(z0)) A__U51(tt, 0, x1) -> c20(A__U52(tt, x1)) A__U51(tt, z0, x1) -> c20(A__ISNAT(z0)) A__U61(tt, 0, x1) -> c26(A__U62(tt, x1)) A__U61(tt, z0, x1) -> c26(A__ISNAT(z0)) A__U71(tt, isNatList(z0)) -> c32(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) A__U71(tt, U21(z0, z1)) -> c32(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) A__U71(tt, U22(z0)) -> c32(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) A__U71(tt, isNat(z0)) -> c32(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) A__U71(tt, U31(z0, z1)) -> c32(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U71(tt, U32(z0)) -> c32(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) A__U71(tt, U41(z0, z1, z2)) -> c32(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) A__U71(tt, U42(z0, z1)) -> c32(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) A__U71(tt, U43(z0)) -> c32(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) A__U71(tt, isNatIList(z0)) -> c32(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) A__U71(tt, U51(z0, z1, z2)) -> c32(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U71(tt, U52(z0, z1)) -> c32(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) A__U71(tt, U53(z0)) -> c32(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) A__U71(tt, U61(z0, z1, z2)) -> c32(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) A__U71(tt, U62(z0, z1)) -> c32(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) A__U71(tt, U63(z0)) -> c32(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) A__U71(tt, U71(z0, z1)) -> c32(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) A__U71(tt, length(z0)) -> c32(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) A__U71(tt, U81(z0)) -> c32(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) A__U71(tt, U91(z0, z1, z2, z3)) -> c32(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) A__U71(tt, take(z0, z1)) -> c32(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) A__U71(tt, and(z0, z1)) -> c32(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U71(tt, isNatIListKind(z0)) -> c32(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) A__U71(tt, isNatKind(z0)) -> c32(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) A__U71(tt, cons(z0, z1)) -> c32(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__U71(tt, zeros) -> c32(A__LENGTH(a__zeros)) A__U71(tt, s(z0)) -> c32(MARK(s(z0))) A__ISNAT(length(cons(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNAT(length(take(z0, z1))) -> c41(A__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNAT(length(nil)) -> c41(A__U11(tt, nil)) A__ISNAT(length(zeros)) -> c41(A__U11(tt, zeros)) A__ISNAT(length(z0)) -> c41(A__ISNATILISTKIND(z0)) A__ISNAT(s(length(z0))) -> c42(A__U21(a__isNatIListKind(z0), length(z0)), A__ISNATKIND(length(z0))) A__ISNAT(s(s(z0))) -> c42(A__U21(a__isNatKind(z0), s(z0)), A__ISNATKIND(s(z0))) A__ISNAT(s(0)) -> c42(A__U21(tt, 0)) A__ISNAT(s(z0)) -> c42(A__ISNATKIND(z0)) A__ISNATILIST(cons(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), A__ISNATILISTKIND(cons(z0, z1))) A__ISNATILIST(take(z0, z1)) -> c44(A__U31(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), A__ISNATILISTKIND(take(z0, z1))) A__ISNATILIST(nil) -> c44(A__U31(tt, nil)) A__ISNATILIST(zeros) -> c44(A__U31(tt, zeros)) A__ISNATILIST(z0) -> c44(A__ISNATILISTKIND(z0)) A__ISNATILIST(cons(length(z0), x1)) -> c46(A__U41(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILIST(cons(s(z0), x1)) -> c46(A__U41(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILIST(cons(z0, x1)) -> c46(A__U41(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATILIST(cons(x0, x1)) -> c46(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATILIST(cons(0, x1)) -> c46(A__U41(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATILISTKIND(cons(length(z0), x1)) -> c50(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(cons(s(z0), x1)) -> c50(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(cons(0, x1)) -> c50(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(cons(z0, x1)) -> c50(A__ISNATKIND(z0)) A__ISNATILISTKIND(take(length(z0), x1)) -> c51(A__AND(a__isNatIListKind(z0), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATILISTKIND(take(s(z0), x1)) -> c51(A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATILISTKIND(take(0, x1)) -> c51(A__AND(tt, isNatIListKind(x1))) A__ISNATILISTKIND(take(z0, x1)) -> c51(A__ISNATKIND(z0)) A__ISNATLIST(cons(length(z0), x1)) -> c58(A__U51(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(cons(s(z0), x1)) -> c58(A__U51(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(cons(z0, x1)) -> c58(A__U51(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(cons(x0, x1)) -> c58(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(cons(0, x1)) -> c58(A__U51(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__ISNATLIST(take(length(z0), x1)) -> c59(A__U61(a__and(a__isNatIListKind(z0), isNatIListKind(x1)), length(z0), x1), A__AND(a__isNatKind(length(z0)), isNatIListKind(x1)), A__ISNATKIND(length(z0))) A__ISNATLIST(take(s(z0), x1)) -> c59(A__U61(a__and(a__isNatKind(z0), isNatIListKind(x1)), s(z0), x1), A__AND(a__isNatKind(s(z0)), isNatIListKind(x1)), A__ISNATKIND(s(z0))) A__ISNATLIST(take(z0, x1)) -> c59(A__U61(a__and(isNatKind(z0), isNatIListKind(x1)), z0, x1), A__AND(a__isNatKind(z0), isNatIListKind(x1)), A__ISNATKIND(z0)) A__ISNATLIST(take(x0, x1)) -> c59(A__AND(a__isNatKind(x0), isNatIListKind(x1)), A__ISNATKIND(x0)) A__ISNATLIST(take(0, x1)) -> c59(A__U61(a__and(tt, isNatIListKind(x1)), 0, x1), A__AND(a__isNatKind(0), isNatIListKind(x1))) A__LENGTH(cons(x0, x1)) -> c62(A__U71(a__and(and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), x1), A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, cons(z0, z1))) -> c62(A__U71(a__and(a__and(a__U51(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), cons(z0, z1)), A__AND(a__and(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATLIST(cons(z0, z1))) A__LENGTH(cons(x0, take(z0, z1))) -> c62(A__U71(a__and(a__and(a__U61(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), take(z0, z1)), A__AND(a__and(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(take(z0, z1)), isNatIListKind(take(z0, z1))), A__ISNATLIST(take(z0, z1))) A__LENGTH(cons(x0, z0)) -> c62(A__U71(a__and(a__and(isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), z0), A__AND(a__and(a__isNatList(z0), isNatIListKind(z0)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(z0), isNatIListKind(z0)), A__ISNATLIST(z0)) A__LENGTH(cons(x0, x1)) -> c62(A__AND(a__and(a__isNatList(x1), isNatIListKind(x1)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(x1), isNatIListKind(x1)), A__ISNATLIST(x1)) A__LENGTH(cons(x0, nil)) -> c62(A__AND(a__and(a__isNatList(nil), isNatIListKind(nil)), and(isNat(x0), isNatKind(x0))), A__AND(a__isNatList(nil), isNatIListKind(nil))) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__U91(a__and(and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), x2, x0, x1), A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, zeros)) -> c65(A__U91(a__and(a__and(tt, isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), zeros, x0, x1), A__AND(a__and(a__isNatIList(zeros), isNatIListKind(zeros)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(zeros), isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(s(x0), cons(x1, cons(z0, z1))) -> c65(A__U91(a__and(a__and(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), cons(z0, z1), x0, x1), A__AND(a__and(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(cons(z0, z1)), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(s(x0), cons(x1, z0)) -> c65(A__U91(a__and(a__and(isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), z0, x0, x1), A__AND(a__and(a__isNatIList(z0), isNatIListKind(z0)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(s(x0), cons(x1, x2)) -> c65(A__AND(a__and(a__isNatIList(x2), isNatIListKind(x2)), and(and(isNat(x0), isNatKind(x0)), and(isNat(x1), isNatKind(x1)))), A__AND(a__isNatIList(x2), isNatIListKind(x2)), A__ISNATILIST(x2)) MARK(U11(U11(z0, z1), x1)) -> c68(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c68(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNatList(z0), x1)) -> c68(A__U11(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U11(U21(z0, z1), x1)) -> c68(A__U11(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U11(U22(z0), x1)) -> c68(A__U11(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U11(isNat(z0), x1)) -> c68(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U31(z0, z1), x1)) -> c68(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c68(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1, z2), x1)) -> c68(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1), x1)) -> c68(A__U11(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U11(U43(z0), x1)) -> c68(A__U11(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U11(isNatIList(z0), x1)) -> c68(A__U11(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U11(U51(z0, z1, z2), x1)) -> c68(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1), x1)) -> c68(A__U11(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U11(U53(z0), x1)) -> c68(A__U11(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U11(U61(z0, z1, z2), x1)) -> c68(A__U11(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U11(U62(z0, z1), x1)) -> c68(A__U11(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U11(U63(z0), x1)) -> c68(A__U11(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U11(U71(z0, z1), x1)) -> c68(A__U11(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U11(length(z0), x1)) -> c68(A__U11(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U11(U81(z0), x1)) -> c68(A__U11(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U11(U91(z0, z1, z2, z3), x1)) -> c68(A__U11(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U11(take(z0, z1), x1)) -> c68(A__U11(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c68(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNatIListKind(z0), x1)) -> c68(A__U11(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U11(isNatKind(z0), x1)) -> c68(A__U11(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U11(zeros, x1)) -> c68(A__U11(a__zeros, x1)) MARK(U11(cons(z0, z1), x1)) -> c68(MARK(cons(z0, z1))) MARK(U11(tt, x1)) -> c68(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c68(MARK(s(z0))) MARK(U21(U11(z0, z1), x1)) -> c71(A__U21(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U21(U12(z0), x1)) -> c71(A__U21(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U21(isNatList(z0), x1)) -> c71(A__U21(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U21(U21(z0, z1), x1)) -> c71(A__U21(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U21(U22(z0), x1)) -> c71(A__U21(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U21(isNat(z0), x1)) -> c71(A__U21(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U21(U31(z0, z1), x1)) -> c71(A__U21(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U21(U32(z0), x1)) -> c71(A__U21(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U21(U41(z0, z1, z2), x1)) -> c71(A__U21(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1), x1)) -> c71(A__U21(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U21(U43(z0), x1)) -> c71(A__U21(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U21(isNatIList(z0), x1)) -> c71(A__U21(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U21(U51(z0, z1, z2), x1)) -> c71(A__U21(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U21(U52(z0, z1), x1)) -> c71(A__U21(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U21(U53(z0), x1)) -> c71(A__U21(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U21(U61(z0, z1, z2), x1)) -> c71(A__U21(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U21(U62(z0, z1), x1)) -> c71(A__U21(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U21(U63(z0), x1)) -> c71(A__U21(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U21(U71(z0, z1), x1)) -> c71(A__U21(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U21(length(z0), x1)) -> c71(A__U21(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U21(U81(z0), x1)) -> c71(A__U21(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U21(U91(z0, z1, z2, z3), x1)) -> c71(A__U21(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U21(take(z0, z1), x1)) -> c71(A__U21(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U21(and(z0, z1), x1)) -> c71(A__U21(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U21(isNatIListKind(z0), x1)) -> c71(A__U21(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U21(isNatKind(z0), x1)) -> c71(A__U21(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U21(zeros, x1)) -> c71(A__U21(a__zeros, x1)) MARK(U21(cons(z0, z1), x1)) -> c71(MARK(cons(z0, z1))) MARK(U21(tt, x1)) -> c71(A__U21(tt, x1)) MARK(U21(s(z0), x1)) -> c71(MARK(s(z0))) MARK(U31(U11(z0, z1), x1)) -> c74(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c74(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNatList(z0), x1)) -> c74(A__U31(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U31(U21(z0, z1), x1)) -> c74(A__U31(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U31(U22(z0), x1)) -> c74(A__U31(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U31(isNat(z0), x1)) -> c74(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U31(z0, z1), x1)) -> c74(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c74(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1, z2), x1)) -> c74(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1), x1)) -> c74(A__U31(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U31(U43(z0), x1)) -> c74(A__U31(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U31(isNatIList(z0), x1)) -> c74(A__U31(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U31(U51(z0, z1, z2), x1)) -> c74(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1), x1)) -> c74(A__U31(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U31(U53(z0), x1)) -> c74(A__U31(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U31(U61(z0, z1, z2), x1)) -> c74(A__U31(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U31(U62(z0, z1), x1)) -> c74(A__U31(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U31(U63(z0), x1)) -> c74(A__U31(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U31(U71(z0, z1), x1)) -> c74(A__U31(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U31(length(z0), x1)) -> c74(A__U31(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U31(U81(z0), x1)) -> c74(A__U31(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U31(U91(z0, z1, z2, z3), x1)) -> c74(A__U31(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U31(take(z0, z1), x1)) -> c74(A__U31(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U31(and(z0, z1), x1)) -> c74(A__U31(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U31(isNatIListKind(z0), x1)) -> c74(A__U31(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U31(isNatKind(z0), x1)) -> c74(A__U31(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U31(zeros, x1)) -> c74(A__U31(a__zeros, x1)) MARK(U31(cons(z0, z1), x1)) -> c74(MARK(cons(z0, z1))) MARK(U31(tt, x1)) -> c74(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c74(MARK(s(z0))) MARK(U41(U11(z0, z1), x1, x2)) -> c76(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1, x2)) -> c76(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNatList(z0), x1, x2)) -> c76(A__U41(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U41(U21(z0, z1), x1, x2)) -> c76(A__U41(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U41(U22(z0), x1, x2)) -> c76(A__U41(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U41(isNat(z0), x1, x2)) -> c76(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c76(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1, x2)) -> c76(A__U41(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1), x1, x2)) -> c76(A__U41(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U41(U43(z0), x1, x2)) -> c76(A__U41(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U41(isNatIList(z0), x1, x2)) -> c76(A__U41(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U41(U51(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1), x1, x2)) -> c76(A__U41(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U41(U53(z0), x1, x2)) -> c76(A__U41(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U41(U61(z0, z1, z2), x1, x2)) -> c76(A__U41(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U41(U62(z0, z1), x1, x2)) -> c76(A__U41(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U41(U63(z0), x1, x2)) -> c76(A__U41(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U41(U71(z0, z1), x1, x2)) -> c76(A__U41(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U41(length(z0), x1, x2)) -> c76(A__U41(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U41(U81(z0), x1, x2)) -> c76(A__U41(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U41(U91(z0, z1, z2, z3), x1, x2)) -> c76(A__U41(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U41(take(z0, z1), x1, x2)) -> c76(A__U41(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U41(and(z0, z1), x1, x2)) -> c76(A__U41(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U41(isNatIListKind(z0), x1, x2)) -> c76(A__U41(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U41(isNatKind(z0), x1, x2)) -> c76(A__U41(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U41(zeros, x1, x2)) -> c76(A__U41(a__zeros, x1, x2)) MARK(U41(cons(z0, z1), x1, x2)) -> c76(MARK(cons(z0, z1))) MARK(U41(tt, x1, x2)) -> c76(A__U41(tt, x1, x2)) MARK(U41(s(z0), x1, x2)) -> c76(MARK(s(z0))) MARK(U42(U11(z0, z1), x1)) -> c77(A__U42(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U42(U12(z0), x1)) -> c77(A__U42(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U42(isNatList(z0), x1)) -> c77(A__U42(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U42(U21(z0, z1), x1)) -> c77(A__U42(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U42(U22(z0), x1)) -> c77(A__U42(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U42(isNat(z0), x1)) -> c77(A__U42(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U42(U31(z0, z1), x1)) -> c77(A__U42(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U42(U32(z0), x1)) -> c77(A__U42(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U42(U41(z0, z1, z2), x1)) -> c77(A__U42(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1), x1)) -> c77(A__U42(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U42(U43(z0), x1)) -> c77(A__U42(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U42(isNatIList(z0), x1)) -> c77(A__U42(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U42(U51(z0, z1, z2), x1)) -> c77(A__U42(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U42(U52(z0, z1), x1)) -> c77(A__U42(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U42(U53(z0), x1)) -> c77(A__U42(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U42(U61(z0, z1, z2), x1)) -> c77(A__U42(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U42(U62(z0, z1), x1)) -> c77(A__U42(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U42(U63(z0), x1)) -> c77(A__U42(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U42(U71(z0, z1), x1)) -> c77(A__U42(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U42(length(z0), x1)) -> c77(A__U42(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U42(U81(z0), x1)) -> c77(A__U42(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U42(U91(z0, z1, z2, z3), x1)) -> c77(A__U42(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U42(take(z0, z1), x1)) -> c77(A__U42(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U42(and(z0, z1), x1)) -> c77(A__U42(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U42(isNatIListKind(z0), x1)) -> c77(A__U42(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U42(isNatKind(z0), x1)) -> c77(A__U42(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U42(zeros, x1)) -> c77(A__U42(a__zeros, x1)) MARK(U42(cons(z0, z1), x1)) -> c77(MARK(cons(z0, z1))) MARK(U42(tt, x1)) -> c77(A__U42(tt, x1)) MARK(U42(s(z0), x1)) -> c77(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c80(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c80(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNatList(z0), x1, x2)) -> c80(A__U51(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U51(U21(z0, z1), x1, x2)) -> c80(A__U51(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U51(U22(z0), x1, x2)) -> c80(A__U51(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U51(isNat(z0), x1, x2)) -> c80(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c80(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c80(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U51(U42(z0, z1), x1, x2)) -> c80(A__U51(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U51(U43(z0), x1, x2)) -> c80(A__U51(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U51(isNatIList(z0), x1, x2)) -> c80(A__U51(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1), x1, x2)) -> c80(A__U51(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U51(U53(z0), x1, x2)) -> c80(A__U51(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U51(U61(z0, z1, z2), x1, x2)) -> c80(A__U51(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U51(U62(z0, z1), x1, x2)) -> c80(A__U51(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U51(U63(z0), x1, x2)) -> c80(A__U51(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U51(U71(z0, z1), x1, x2)) -> c80(A__U51(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U51(length(z0), x1, x2)) -> c80(A__U51(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U51(U81(z0), x1, x2)) -> c80(A__U51(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U51(U91(z0, z1, z2, z3), x1, x2)) -> c80(A__U51(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U51(take(z0, z1), x1, x2)) -> c80(A__U51(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U51(and(z0, z1), x1, x2)) -> c80(A__U51(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U51(isNatIListKind(z0), x1, x2)) -> c80(A__U51(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U51(isNatKind(z0), x1, x2)) -> c80(A__U51(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U51(zeros, x1, x2)) -> c80(A__U51(a__zeros, x1, x2)) MARK(U51(cons(z0, z1), x1, x2)) -> c80(MARK(cons(z0, z1))) MARK(U51(tt, x1, x2)) -> c80(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c80(MARK(s(z0))) MARK(U52(U11(z0, z1), x1)) -> c81(A__U52(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1)) -> c81(A__U52(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U52(isNatList(z0), x1)) -> c81(A__U52(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U52(U21(z0, z1), x1)) -> c81(A__U52(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U52(U22(z0), x1)) -> c81(A__U52(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U52(isNat(z0), x1)) -> c81(A__U52(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U52(U31(z0, z1), x1)) -> c81(A__U52(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1)) -> c81(A__U52(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U52(U41(z0, z1, z2), x1)) -> c81(A__U52(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U52(U42(z0, z1), x1)) -> c81(A__U52(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U52(U43(z0), x1)) -> c81(A__U52(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U52(isNatIList(z0), x1)) -> c81(A__U52(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U52(U51(z0, z1, z2), x1)) -> c81(A__U52(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1), x1)) -> c81(A__U52(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U52(U53(z0), x1)) -> c81(A__U52(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U52(U61(z0, z1, z2), x1)) -> c81(A__U52(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U52(U62(z0, z1), x1)) -> c81(A__U52(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U52(U63(z0), x1)) -> c81(A__U52(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U52(U71(z0, z1), x1)) -> c81(A__U52(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U52(length(z0), x1)) -> c81(A__U52(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U52(U81(z0), x1)) -> c81(A__U52(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U52(U91(z0, z1, z2, z3), x1)) -> c81(A__U52(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U52(take(z0, z1), x1)) -> c81(A__U52(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U52(and(z0, z1), x1)) -> c81(A__U52(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U52(isNatIListKind(z0), x1)) -> c81(A__U52(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U52(isNatKind(z0), x1)) -> c81(A__U52(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U52(zeros, x1)) -> c81(A__U52(a__zeros, x1)) MARK(U52(cons(z0, z1), x1)) -> c81(MARK(cons(z0, z1))) MARK(U52(tt, x1)) -> c81(A__U52(tt, x1)) MARK(U52(s(z0), x1)) -> c81(MARK(s(z0))) MARK(U61(U11(z0, z1), x1, x2)) -> c83(A__U61(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U61(U12(z0), x1, x2)) -> c83(A__U61(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U61(isNatList(z0), x1, x2)) -> c83(A__U61(a__isNatList(z0), x1, x2), MARK(isNatList(z0))) MARK(U61(U21(z0, z1), x1, x2)) -> c83(A__U61(a__U21(mark(z0), z1), x1, x2), MARK(U21(z0, z1))) MARK(U61(U22(z0), x1, x2)) -> c83(A__U61(a__U22(mark(z0)), x1, x2), MARK(U22(z0))) MARK(U61(isNat(z0), x1, x2)) -> c83(A__U61(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U61(U31(z0, z1), x1, x2)) -> c83(A__U61(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U61(U32(z0), x1, x2)) -> c83(A__U61(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U61(U41(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2))) MARK(U61(U42(z0, z1), x1, x2)) -> c83(A__U61(a__U42(mark(z0), z1), x1, x2), MARK(U42(z0, z1))) MARK(U61(U43(z0), x1, x2)) -> c83(A__U61(a__U43(mark(z0)), x1, x2), MARK(U43(z0))) MARK(U61(isNatIList(z0), x1, x2)) -> c83(A__U61(a__isNatIList(z0), x1, x2), MARK(isNatIList(z0))) MARK(U61(U51(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U61(U52(z0, z1), x1, x2)) -> c83(A__U61(a__U52(mark(z0), z1), x1, x2), MARK(U52(z0, z1))) MARK(U61(U53(z0), x1, x2)) -> c83(A__U61(a__U53(mark(z0)), x1, x2), MARK(U53(z0))) MARK(U61(U61(z0, z1, z2), x1, x2)) -> c83(A__U61(a__U61(mark(z0), z1, z2), x1, x2), MARK(U61(z0, z1, z2))) MARK(U61(U62(z0, z1), x1, x2)) -> c83(A__U61(a__U62(mark(z0), z1), x1, x2), MARK(U62(z0, z1))) MARK(U61(U63(z0), x1, x2)) -> c83(A__U61(a__U63(mark(z0)), x1, x2), MARK(U63(z0))) MARK(U61(U71(z0, z1), x1, x2)) -> c83(A__U61(a__U71(mark(z0), z1), x1, x2), MARK(U71(z0, z1))) MARK(U61(length(z0), x1, x2)) -> c83(A__U61(a__length(mark(z0)), x1, x2), MARK(length(z0))) MARK(U61(U81(z0), x1, x2)) -> c83(A__U61(a__U81(mark(z0)), x1, x2), MARK(U81(z0))) MARK(U61(U91(z0, z1, z2, z3), x1, x2)) -> c83(A__U61(a__U91(mark(z0), z1, z2, z3), x1, x2), MARK(U91(z0, z1, z2, z3))) MARK(U61(take(z0, z1), x1, x2)) -> c83(A__U61(a__take(mark(z0), mark(z1)), x1, x2), MARK(take(z0, z1))) MARK(U61(and(z0, z1), x1, x2)) -> c83(A__U61(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U61(isNatIListKind(z0), x1, x2)) -> c83(A__U61(a__isNatIListKind(z0), x1, x2), MARK(isNatIListKind(z0))) MARK(U61(isNatKind(z0), x1, x2)) -> c83(A__U61(a__isNatKind(z0), x1, x2), MARK(isNatKind(z0))) MARK(U61(zeros, x1, x2)) -> c83(A__U61(a__zeros, x1, x2)) MARK(U61(cons(z0, z1), x1, x2)) -> c83(MARK(cons(z0, z1))) MARK(U61(tt, x1, x2)) -> c83(A__U61(tt, x1, x2)) MARK(U61(s(z0), x1, x2)) -> c83(MARK(s(z0))) MARK(U62(U11(z0, z1), x1)) -> c84(A__U62(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U62(U12(z0), x1)) -> c84(A__U62(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U62(isNatList(z0), x1)) -> c84(A__U62(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U62(U21(z0, z1), x1)) -> c84(A__U62(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U62(U22(z0), x1)) -> c84(A__U62(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U62(isNat(z0), x1)) -> c84(A__U62(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U62(U31(z0, z1), x1)) -> c84(A__U62(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U62(U32(z0), x1)) -> c84(A__U62(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U62(U41(z0, z1, z2), x1)) -> c84(A__U62(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U62(U42(z0, z1), x1)) -> c84(A__U62(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U62(U43(z0), x1)) -> c84(A__U62(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U62(isNatIList(z0), x1)) -> c84(A__U62(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U62(U51(z0, z1, z2), x1)) -> c84(A__U62(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U62(U52(z0, z1), x1)) -> c84(A__U62(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U62(U53(z0), x1)) -> c84(A__U62(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U62(U61(z0, z1, z2), x1)) -> c84(A__U62(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U62(U62(z0, z1), x1)) -> c84(A__U62(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U62(U63(z0), x1)) -> c84(A__U62(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U62(U71(z0, z1), x1)) -> c84(A__U62(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U62(length(z0), x1)) -> c84(A__U62(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U62(U81(z0), x1)) -> c84(A__U62(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U62(U91(z0, z1, z2, z3), x1)) -> c84(A__U62(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U62(take(z0, z1), x1)) -> c84(A__U62(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U62(and(z0, z1), x1)) -> c84(A__U62(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U62(isNatIListKind(z0), x1)) -> c84(A__U62(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U62(isNatKind(z0), x1)) -> c84(A__U62(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U62(zeros, x1)) -> c84(A__U62(a__zeros, x1)) MARK(U62(cons(z0, z1), x1)) -> c84(MARK(cons(z0, z1))) MARK(U62(tt, x1)) -> c84(A__U62(tt, x1)) MARK(U62(s(z0), x1)) -> c84(MARK(s(z0))) MARK(U71(U11(z0, z1), x1)) -> c86(A__U71(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1)) -> c86(A__U71(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U71(isNatList(z0), x1)) -> c86(A__U71(a__isNatList(z0), x1), MARK(isNatList(z0))) MARK(U71(U21(z0, z1), x1)) -> c86(A__U71(a__U21(mark(z0), z1), x1), MARK(U21(z0, z1))) MARK(U71(U22(z0), x1)) -> c86(A__U71(a__U22(mark(z0)), x1), MARK(U22(z0))) MARK(U71(isNat(z0), x1)) -> c86(A__U71(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U71(U31(z0, z1), x1)) -> c86(A__U71(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1)) -> c86(A__U71(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U71(U41(z0, z1, z2), x1)) -> c86(A__U71(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2))) MARK(U71(U42(z0, z1), x1)) -> c86(A__U71(a__U42(mark(z0), z1), x1), MARK(U42(z0, z1))) MARK(U71(U43(z0), x1)) -> c86(A__U71(a__U43(mark(z0)), x1), MARK(U43(z0))) MARK(U71(isNatIList(z0), x1)) -> c86(A__U71(a__isNatIList(z0), x1), MARK(isNatIList(z0))) MARK(U71(U51(z0, z1, z2), x1)) -> c86(A__U71(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1), x1)) -> c86(A__U71(a__U52(mark(z0), z1), x1), MARK(U52(z0, z1))) MARK(U71(U53(z0), x1)) -> c86(A__U71(a__U53(mark(z0)), x1), MARK(U53(z0))) MARK(U71(U61(z0, z1, z2), x1)) -> c86(A__U71(a__U61(mark(z0), z1, z2), x1), MARK(U61(z0, z1, z2))) MARK(U71(U62(z0, z1), x1)) -> c86(A__U71(a__U62(mark(z0), z1), x1), MARK(U62(z0, z1))) MARK(U71(U63(z0), x1)) -> c86(A__U71(a__U63(mark(z0)), x1), MARK(U63(z0))) MARK(U71(U71(z0, z1), x1)) -> c86(A__U71(a__U71(mark(z0), z1), x1), MARK(U71(z0, z1))) MARK(U71(length(z0), x1)) -> c86(A__U71(a__length(mark(z0)), x1), MARK(length(z0))) MARK(U71(U81(z0), x1)) -> c86(A__U71(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(U71(U91(z0, z1, z2, z3), x1)) -> c86(A__U71(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(U71(take(z0, z1), x1)) -> c86(A__U71(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(U71(and(z0, z1), x1)) -> c86(A__U71(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U71(isNatIListKind(z0), x1)) -> c86(A__U71(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(U71(isNatKind(z0), x1)) -> c86(A__U71(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(U71(zeros, x1)) -> c86(A__U71(a__zeros, x1)) MARK(U71(cons(z0, z1), x1)) -> c86(MARK(cons(z0, z1))) MARK(U71(tt, x1)) -> c86(A__U71(tt, x1)) MARK(U71(s(z0), x1)) -> c86(MARK(s(z0))) MARK(length(U11(z0, z1))) -> c87(A__LENGTH(a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(length(U12(z0))) -> c87(A__LENGTH(a__U12(mark(z0))), MARK(U12(z0))) MARK(length(isNatList(z0))) -> c87(A__LENGTH(a__isNatList(z0)), MARK(isNatList(z0))) MARK(length(U21(z0, z1))) -> c87(A__LENGTH(a__U21(mark(z0), z1)), MARK(U21(z0, z1))) MARK(length(U22(z0))) -> c87(A__LENGTH(a__U22(mark(z0))), MARK(U22(z0))) MARK(length(isNat(z0))) -> c87(A__LENGTH(a__isNat(z0)), MARK(isNat(z0))) MARK(length(U31(z0, z1))) -> c87(A__LENGTH(a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(length(U32(z0))) -> c87(A__LENGTH(a__U32(mark(z0))), MARK(U32(z0))) MARK(length(U41(z0, z1, z2))) -> c87(A__LENGTH(a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) MARK(length(U42(z0, z1))) -> c87(A__LENGTH(a__U42(mark(z0), z1)), MARK(U42(z0, z1))) MARK(length(U43(z0))) -> c87(A__LENGTH(a__U43(mark(z0))), MARK(U43(z0))) MARK(length(isNatIList(z0))) -> c87(A__LENGTH(a__isNatIList(z0)), MARK(isNatIList(z0))) MARK(length(U51(z0, z1, z2))) -> c87(A__LENGTH(a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(length(U52(z0, z1))) -> c87(A__LENGTH(a__U52(mark(z0), z1)), MARK(U52(z0, z1))) MARK(length(U53(z0))) -> c87(A__LENGTH(a__U53(mark(z0))), MARK(U53(z0))) MARK(length(U61(z0, z1, z2))) -> c87(A__LENGTH(a__U61(mark(z0), z1, z2)), MARK(U61(z0, z1, z2))) MARK(length(U62(z0, z1))) -> c87(A__LENGTH(a__U62(mark(z0), z1)), MARK(U62(z0, z1))) MARK(length(U63(z0))) -> c87(A__LENGTH(a__U63(mark(z0))), MARK(U63(z0))) MARK(length(U71(z0, z1))) -> c87(A__LENGTH(a__U71(mark(z0), z1)), MARK(U71(z0, z1))) MARK(length(length(z0))) -> c87(A__LENGTH(a__length(mark(z0))), MARK(length(z0))) MARK(length(U81(z0))) -> c87(A__LENGTH(a__U81(mark(z0))), MARK(U81(z0))) MARK(length(U91(z0, z1, z2, z3))) -> c87(A__LENGTH(a__U91(mark(z0), z1, z2, z3)), MARK(U91(z0, z1, z2, z3))) MARK(length(take(z0, z1))) -> c87(A__LENGTH(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(length(and(z0, z1))) -> c87(A__LENGTH(a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(length(isNatIListKind(z0))) -> c87(A__LENGTH(a__isNatIListKind(z0)), MARK(isNatIListKind(z0))) MARK(length(isNatKind(z0))) -> c87(A__LENGTH(a__isNatKind(z0)), MARK(isNatKind(z0))) MARK(length(cons(z0, z1))) -> c87(A__LENGTH(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(length(zeros)) -> c87(A__LENGTH(a__zeros)) MARK(length(s(z0))) -> c87(MARK(s(z0))) MARK(U91(U11(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U11(mark(z0), z1), x1, x2, x3), MARK(U11(z0, z1))) MARK(U91(U12(z0), x1, x2, x3)) -> c89(A__U91(a__U12(mark(z0)), x1, x2, x3), MARK(U12(z0))) MARK(U91(isNatList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatList(z0), x1, x2, x3), MARK(isNatList(z0))) MARK(U91(U21(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U21(mark(z0), z1), x1, x2, x3), MARK(U21(z0, z1))) MARK(U91(U22(z0), x1, x2, x3)) -> c89(A__U91(a__U22(mark(z0)), x1, x2, x3), MARK(U22(z0))) MARK(U91(isNat(z0), x1, x2, x3)) -> c89(A__U91(a__isNat(z0), x1, x2, x3), MARK(isNat(z0))) MARK(U91(U31(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U31(mark(z0), z1), x1, x2, x3), MARK(U31(z0, z1))) MARK(U91(U32(z0), x1, x2, x3)) -> c89(A__U91(a__U32(mark(z0)), x1, x2, x3), MARK(U32(z0))) MARK(U91(U41(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U41(mark(z0), z1, z2), x1, x2, x3), MARK(U41(z0, z1, z2))) MARK(U91(U42(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U42(mark(z0), z1), x1, x2, x3), MARK(U42(z0, z1))) MARK(U91(U43(z0), x1, x2, x3)) -> c89(A__U91(a__U43(mark(z0)), x1, x2, x3), MARK(U43(z0))) MARK(U91(isNatIList(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIList(z0), x1, x2, x3), MARK(isNatIList(z0))) MARK(U91(U51(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U51(mark(z0), z1, z2), x1, x2, x3), MARK(U51(z0, z1, z2))) MARK(U91(U52(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U52(mark(z0), z1), x1, x2, x3), MARK(U52(z0, z1))) MARK(U91(U53(z0), x1, x2, x3)) -> c89(A__U91(a__U53(mark(z0)), x1, x2, x3), MARK(U53(z0))) MARK(U91(U61(z0, z1, z2), x1, x2, x3)) -> c89(A__U91(a__U61(mark(z0), z1, z2), x1, x2, x3), MARK(U61(z0, z1, z2))) MARK(U91(U62(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U62(mark(z0), z1), x1, x2, x3), MARK(U62(z0, z1))) MARK(U91(U63(z0), x1, x2, x3)) -> c89(A__U91(a__U63(mark(z0)), x1, x2, x3), MARK(U63(z0))) MARK(U91(U71(z0, z1), x1, x2, x3)) -> c89(A__U91(a__U71(mark(z0), z1), x1, x2, x3), MARK(U71(z0, z1))) MARK(U91(length(z0), x1, x2, x3)) -> c89(A__U91(a__length(mark(z0)), x1, x2, x3), MARK(length(z0))) MARK(U91(U81(z0), x1, x2, x3)) -> c89(A__U91(a__U81(mark(z0)), x1, x2, x3), MARK(U81(z0))) MARK(U91(U91(z0, z1, z2, z3), x1, x2, x3)) -> c89(A__U91(a__U91(mark(z0), z1, z2, z3), x1, x2, x3), MARK(U91(z0, z1, z2, z3))) MARK(U91(take(z0, z1), x1, x2, x3)) -> c89(A__U91(a__take(mark(z0), mark(z1)), x1, x2, x3), MARK(take(z0, z1))) MARK(U91(and(z0, z1), x1, x2, x3)) -> c89(A__U91(a__and(mark(z0), z1), x1, x2, x3), MARK(and(z0, z1))) MARK(U91(isNatIListKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatIListKind(z0), x1, x2, x3), MARK(isNatIListKind(z0))) MARK(U91(isNatKind(z0), x1, x2, x3)) -> c89(A__U91(a__isNatKind(z0), x1, x2, x3), MARK(isNatKind(z0))) MARK(U91(zeros, x1, x2, x3)) -> c89(A__U91(a__zeros, x1, x2, x3)) MARK(U91(cons(z0, z1), x1, x2, x3)) -> c89(MARK(cons(z0, z1))) MARK(U91(tt, x1, x2, x3)) -> c89(A__U91(tt, x1, x2, x3)) MARK(U91(s(z0), x1, x2, x3)) -> c89(MARK(s(z0))) MARK(take(x0, zeros)) -> c90(A__TAKE(mark(x0), a__zeros), MARK(x0)) MARK(take(x0, U11(z0, z1))) -> c90(A__TAKE(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(take(x0, U12(z0))) -> c90(A__TAKE(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(take(x0, isNatList(z0))) -> c90(A__TAKE(mark(x0), a__isNatList(z0)), MARK(x0)) MARK(take(x0, U21(z0, z1))) -> c90(A__TAKE(mark(x0), a__U21(mark(z0), z1)), MARK(x0)) MARK(take(x0, U22(z0))) -> c90(A__TAKE(mark(x0), a__U22(mark(z0))), MARK(x0)) MARK(take(x0, isNat(z0))) -> c90(A__TAKE(mark(x0), a__isNat(z0)), MARK(x0)) MARK(take(x0, U31(z0, z1))) -> c90(A__TAKE(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(take(x0, U32(z0))) -> c90(A__TAKE(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(take(x0, U41(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U42(z0, z1))) -> c90(A__TAKE(mark(x0), a__U42(mark(z0), z1)), MARK(x0)) MARK(take(x0, U43(z0))) -> c90(A__TAKE(mark(x0), a__U43(mark(z0))), MARK(x0)) MARK(take(x0, isNatIList(z0))) -> c90(A__TAKE(mark(x0), a__isNatIList(z0)), MARK(x0)) MARK(take(x0, U51(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U52(z0, z1))) -> c90(A__TAKE(mark(x0), a__U52(mark(z0), z1)), MARK(x0)) MARK(take(x0, U53(z0))) -> c90(A__TAKE(mark(x0), a__U53(mark(z0))), MARK(x0)) MARK(take(x0, U61(z0, z1, z2))) -> c90(A__TAKE(mark(x0), a__U61(mark(z0), z1, z2)), MARK(x0)) MARK(take(x0, U62(z0, z1))) -> c90(A__TAKE(mark(x0), a__U62(mark(z0), z1)), MARK(x0)) MARK(take(x0, U63(z0))) -> c90(A__TAKE(mark(x0), a__U63(mark(z0))), MARK(x0)) MARK(take(x0, U71(z0, z1))) -> c90(A__TAKE(mark(x0), a__U71(mark(z0), z1)), MARK(x0)) MARK(take(x0, length(z0))) -> c90(A__TAKE(mark(x0), a__length(mark(z0))), MARK(x0)) MARK(take(x0, U81(z0))) -> c90(A__TAKE(mark(x0), a__U81(mark(z0))), MARK(x0)) MARK(take(x0, U91(z0, z1, z2, z3))) -> c90(A__TAKE(mark(x0), a__U91(mark(z0), z1, z2, z3)), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c90(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, and(z0, z1))) -> c90(A__TAKE(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(take(x0, isNatIListKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatIListKind(z0)), MARK(x0)) MARK(take(x0, isNatKind(z0))) -> c90(A__TAKE(mark(x0), a__isNatKind(z0)), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c90(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c90(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, tt)) -> c90(A__TAKE(mark(x0), tt), MARK(x0)) MARK(take(x0, s(z0))) -> c90(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c90(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(U11(z0, z1), x1)) -> c90(A__TAKE(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(take(U12(z0), x1)) -> c90(A__TAKE(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(take(isNatList(z0), x1)) -> c90(A__TAKE(a__isNatList(z0), mark(x1)), MARK(isNatList(z0))) MARK(take(U21(z0, z1), x1)) -> c90(A__TAKE(a__U21(mark(z0), z1), mark(x1)), MARK(U21(z0, z1))) MARK(take(U22(z0), x1)) -> c90(A__TAKE(a__U22(mark(z0)), mark(x1)), MARK(U22(z0))) MARK(take(isNat(z0), x1)) -> c90(A__TAKE(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(take(U31(z0, z1), x1)) -> c90(A__TAKE(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(take(U32(z0), x1)) -> c90(A__TAKE(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(take(U41(z0, z1, z2), x1)) -> c90(A__TAKE(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2))) MARK(take(U42(z0, z1), x1)) -> c90(A__TAKE(a__U42(mark(z0), z1), mark(x1)), MARK(U42(z0, z1))) MARK(take(U43(z0), x1)) -> c90(A__TAKE(a__U43(mark(z0)), mark(x1)), MARK(U43(z0))) MARK(take(isNatIList(z0), x1)) -> c90(A__TAKE(a__isNatIList(z0), mark(x1)), MARK(isNatIList(z0))) MARK(take(U51(z0, z1, z2), x1)) -> c90(A__TAKE(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(take(U52(z0, z1), x1)) -> c90(A__TAKE(a__U52(mark(z0), z1), mark(x1)), MARK(U52(z0, z1))) MARK(take(U53(z0), x1)) -> c90(A__TAKE(a__U53(mark(z0)), mark(x1)), MARK(U53(z0))) MARK(take(U61(z0, z1, z2), x1)) -> c90(A__TAKE(a__U61(mark(z0), z1, z2), mark(x1)), MARK(U61(z0, z1, z2))) MARK(take(U62(z0, z1), x1)) -> c90(A__TAKE(a__U62(mark(z0), z1), mark(x1)), MARK(U62(z0, z1))) MARK(take(U63(z0), x1)) -> c90(A__TAKE(a__U63(mark(z0)), mark(x1)), MARK(U63(z0))) MARK(take(U71(z0, z1), x1)) -> c90(A__TAKE(a__U71(mark(z0), z1), mark(x1)), MARK(U71(z0, z1))) MARK(take(length(z0), x1)) -> 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MARK(length(z0))) MARK(and(U81(z0), x1)) -> c92(A__AND(a__U81(mark(z0)), x1), MARK(U81(z0))) MARK(and(U91(z0, z1, z2, z3), x1)) -> c92(A__AND(a__U91(mark(z0), z1, z2, z3), x1), MARK(U91(z0, z1, z2, z3))) MARK(and(take(z0, z1), x1)) -> c92(A__AND(a__take(mark(z0), mark(z1)), x1), MARK(take(z0, z1))) MARK(and(and(z0, z1), x1)) -> c92(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNatIListKind(z0), x1)) -> c92(A__AND(a__isNatIListKind(z0), x1), MARK(isNatIListKind(z0))) MARK(and(isNatKind(z0), x1)) -> c92(A__AND(a__isNatKind(z0), x1), MARK(isNatKind(z0))) MARK(and(zeros, x1)) -> c92(A__AND(a__zeros, x1)) MARK(and(cons(z0, z1), x1)) -> c92(MARK(cons(z0, z1))) MARK(and(tt, x1)) -> c92(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c92(MARK(s(z0))) A__TAKE(0, z0) -> c64(A__AND(a__U31(a__isNatIListKind(z0), z0), isNatIListKind(z0)), A__ISNATILIST(z0)) A__TAKE(0, zeros) -> c64(A__AND(tt, isNatIListKind(zeros)), A__ISNATILIST(zeros)) A__TAKE(0, cons(z0, z1)) -> c64(A__AND(a__U41(a__and(a__isNatKind(z0), isNatIListKind(z1)), z0, z1), isNatIListKind(cons(z0, z1))), A__ISNATILIST(cons(z0, z1))) A__TAKE(0, z0) -> c64(A__ISNATILIST(z0)) A__U41(tt, length(nil), x1) -> c14(A__U42(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U41(tt, length(zeros), x1) -> c14(A__U42(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U41(tt, length(cons(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U41(tt, length(take(z0, z1)), x1) -> c14(A__U42(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U41(tt, length(z0), x1) -> c14(A__U42(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U41(tt, length(z1), x1) -> c14(A__ISNAT(length(z1))) A__U41(tt, s(0), x1) -> c14(A__U42(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U41(tt, s(length(z0)), x1) -> c14(A__U42(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U41(tt, s(s(z0)), x1) -> c14(A__U42(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U41(tt, s(z0), x1) -> c14(A__U42(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U41(tt, s(z1), x1) -> c14(A__ISNAT(s(z1))) A__U51(tt, length(nil), x1) -> c20(A__U52(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U51(tt, length(zeros), x1) -> c20(A__U52(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U51(tt, length(cons(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U51(tt, length(take(z0, z1)), x1) -> c20(A__U52(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U51(tt, length(z0), x1) -> c20(A__U52(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U51(tt, length(z1), x1) -> c20(A__ISNAT(length(z1))) A__U51(tt, s(0), x1) -> c20(A__U52(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U51(tt, s(length(z0)), x1) -> c20(A__U52(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U51(tt, s(s(z0)), x1) -> c20(A__U52(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U51(tt, s(z0), x1) -> c20(A__U52(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U51(tt, s(z1), x1) -> c20(A__ISNAT(s(z1))) A__U61(tt, length(nil), x1) -> c26(A__U62(a__U11(tt, nil), x1), A__ISNAT(length(nil))) A__U61(tt, length(zeros), x1) -> c26(A__U62(a__U11(tt, zeros), x1), A__ISNAT(length(zeros))) A__U61(tt, length(cons(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), cons(z0, z1)), x1), A__ISNAT(length(cons(z0, z1)))) A__U61(tt, length(take(z0, z1)), x1) -> c26(A__U62(a__U11(a__and(a__isNatKind(z0), isNatIListKind(z1)), take(z0, z1)), x1), A__ISNAT(length(take(z0, z1)))) A__U61(tt, length(z0), x1) -> c26(A__U62(a__U11(isNatIListKind(z0), z0), x1), A__ISNAT(length(z0))) A__U61(tt, length(z1), x1) -> c26(A__ISNAT(length(z1))) A__U61(tt, s(0), x1) -> c26(A__U62(a__U21(tt, 0), x1), A__ISNAT(s(0))) A__U61(tt, s(length(z0)), x1) -> c26(A__U62(a__U21(a__isNatIListKind(z0), length(z0)), x1), A__ISNAT(s(length(z0)))) A__U61(tt, s(s(z0)), x1) -> c26(A__U62(a__U21(a__isNatKind(z0), s(z0)), x1), A__ISNAT(s(s(z0)))) A__U61(tt, s(z0), x1) -> c26(A__U62(a__U21(isNatKind(z0), z0), x1), A__ISNAT(s(z0))) A__U61(tt, s(z1), x1) -> c26(A__ISNAT(s(z1))) A__U71(tt, U11(zeros, x1)) -> c32(A__LENGTH(a__U11(a__zeros, x1)), MARK(U11(zeros, x1))) A__U71(tt, U11(U11(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U71(tt, U11(U12(z0), x1)) -> c32(A__LENGTH(a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1))) A__U71(tt, U11(isNatList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatList(z0), x1)), MARK(U11(isNatList(z0), x1))) A__U71(tt, U11(U21(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U21(mark(z0), z1), x1)), MARK(U11(U21(z0, z1), x1))) A__U71(tt, U11(U22(z0), x1)) -> c32(A__LENGTH(a__U11(a__U22(mark(z0)), x1)), MARK(U11(U22(z0), x1))) A__U71(tt, U11(isNat(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U71(tt, U11(U31(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1))) A__U71(tt, U11(U32(z0), x1)) -> c32(A__LENGTH(a__U11(a__U32(mark(z0)), x1)), MARK(U11(U32(z0), x1))) A__U71(tt, U11(U41(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1))) A__U71(tt, U11(U42(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U42(mark(z0), z1), x1)), MARK(U11(U42(z0, z1), x1))) A__U71(tt, U11(U43(z0), x1)) -> c32(A__LENGTH(a__U11(a__U43(mark(z0)), x1)), MARK(U11(U43(z0), x1))) A__U71(tt, U11(isNatIList(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIList(z0), x1)), MARK(U11(isNatIList(z0), x1))) A__U71(tt, U11(U51(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(U11(U51(z0, z1, z2), x1))) A__U71(tt, U11(U52(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U52(mark(z0), z1), x1)), MARK(U11(U52(z0, z1), x1))) A__U71(tt, U11(U53(z0), x1)) -> c32(A__LENGTH(a__U11(a__U53(mark(z0)), x1)), MARK(U11(U53(z0), x1))) A__U71(tt, U11(U61(z0, z1, z2), x1)) -> c32(A__LENGTH(a__U11(a__U61(mark(z0), z1, z2), x1)), MARK(U11(U61(z0, z1, z2), x1))) A__U71(tt, U11(U62(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U62(mark(z0), z1), x1)), MARK(U11(U62(z0, z1), x1))) A__U71(tt, U11(U63(z0), x1)) -> c32(A__LENGTH(a__U11(a__U63(mark(z0)), x1)), MARK(U11(U63(z0), x1))) A__U71(tt, U11(U71(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__U71(mark(z0), z1), x1)), MARK(U11(U71(z0, z1), x1))) A__U71(tt, U11(length(z0), x1)) -> c32(A__LENGTH(a__U11(a__length(mark(z0)), x1)), MARK(U11(length(z0), x1))) A__U71(tt, U11(U81(z0), x1)) -> c32(A__LENGTH(a__U11(a__U81(mark(z0)), x1)), MARK(U11(U81(z0), x1))) A__U71(tt, U11(U91(z0, z1, z2, z3), x1)) -> c32(A__LENGTH(a__U11(a__U91(mark(z0), z1, z2, z3), x1)), MARK(U11(U91(z0, z1, z2, z3), x1))) A__U71(tt, U11(take(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__take(mark(z0), mark(z1)), x1)), MARK(U11(take(z0, z1), x1))) A__U71(tt, U11(and(z0, z1), x1)) -> c32(A__LENGTH(a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U71(tt, U11(isNatIListKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatIListKind(z0), x1)), MARK(U11(isNatIListKind(z0), x1))) A__U71(tt, U11(isNatKind(z0), x1)) -> c32(A__LENGTH(a__U11(a__isNatKind(z0), x1)), MARK(U11(isNatKind(z0), x1))) A__U71(tt, U11(cons(z0, z1), x1)) -> c32(A__LENGTH(a__U11(cons(mark(z0), z1), x1)), MARK(U11(cons(z0, z1), x1))) A__U71(tt, U11(tt, x1)) -> c32(A__LENGTH(a__U11(tt, x1)), MARK(U11(tt, x1))) A__U71(tt, U11(s(z0), x1)) -> c32(A__LENGTH(a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U71(tt, U11(x0, z1)) -> c32(MARK(U11(x0, z1))) A__U71(tt, U11(0, x1)) -> c32(A__LENGTH(a__U11(0, x1))) A__U71(tt, U11(nil, x1)) -> c32(A__LENGTH(a__U11(nil, x1))) A__U71(tt, U12(zeros)) -> c32(A__LENGTH(a__U12(a__zeros)), MARK(U12(zeros))) A__U71(tt, U12(U11(z0, z1))) -> c32(A__LENGTH(a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1)))) A__U71(tt, U12(U12(z0))) -> c32(A__LENGTH(a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0)))) A__U71(tt, U12(isNatList(z0))) -> c32(A__LENGTH(a__U12(a__isNatList(z0))), MARK(U12(isNatList(z0)))) A__U71(tt, U12(U21(z0, z1))) -> c32(A__LENGTH(a__U12(a__U21(mark(z0), z1))), MARK(U12(U21(z0, z1)))) A__U71(tt, U12(U22(z0))) -> c32(A__LENGTH(a__U12(a__U22(mark(z0)))), MARK(U12(U22(z0)))) A__U71(tt, U12(isNat(z0))) -> c32(A__LENGTH(a__U12(a__isNat(z0))), MARK(U12(isNat(z0)))) A__U71(tt, U12(U31(z0, z1))) -> c32(A__LENGTH(a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1)))) A__U71(tt, U12(U32(z0))) -> c32(A__LENGTH(a__U12(a__U32(mark(z0)))), MARK(U12(U32(z0)))) A__U71(tt, U12(U41(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2)))) A__U71(tt, U12(U42(z0, z1))) -> c32(A__LENGTH(a__U12(a__U42(mark(z0), z1))), MARK(U12(U42(z0, z1)))) A__U71(tt, U12(U43(z0))) -> c32(A__LENGTH(a__U12(a__U43(mark(z0)))), MARK(U12(U43(z0)))) A__U71(tt, U12(isNatIList(z0))) -> c32(A__LENGTH(a__U12(a__isNatIList(z0))), MARK(U12(isNatIList(z0)))) A__U71(tt, U12(U51(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U51(mark(z0), z1, z2))), MARK(U12(U51(z0, z1, z2)))) A__U71(tt, U12(U52(z0, z1))) -> c32(A__LENGTH(a__U12(a__U52(mark(z0), z1))), MARK(U12(U52(z0, z1)))) A__U71(tt, U12(U53(z0))) -> c32(A__LENGTH(a__U12(a__U53(mark(z0)))), MARK(U12(U53(z0)))) A__U71(tt, U12(U61(z0, z1, z2))) -> c32(A__LENGTH(a__U12(a__U61(mark(z0), z1, z2))), MARK(U12(U61(z0, z1, z2)))) A__U71(tt, U12(U62(z0, z1))) -> c32(A__LENGTH(a__U12(a__U62(mark(z0), z1))), MARK(U12(U62(z0, z1)))) A__U71(tt, U12(U63(z0))) -> c32(A__LENGTH(a__U12(a__U63(mark(z0)))), MARK(U12(U63(z0)))) A__U71(tt, U12(U71(z0, z1))) -> c32(A__LENGTH(a__U12(a__U71(mark(z0), z1))), MARK(U12(U71(z0, z1)))) A__U71(tt, U12(length(z0))) -> c32(A__LENGTH(a__U12(a__length(mark(z0)))), MARK(U12(length(z0)))) A__U71(tt, U12(U81(z0))) -> c32(A__LENGTH(a__U12(a__U81(mark(z0)))), MARK(U12(U81(z0)))) A__U71(tt, U12(U91(z0, z1, z2, z3))) -> c32(A__LENGTH(a__U12(a__U91(mark(z0), z1, z2, z3))), MARK(U12(U91(z0, z1, z2, z3)))) A__U71(tt, U12(take(z0, z1))) -> c32(A__LENGTH(a__U12(a__take(mark(z0), mark(z1)))), MARK(U12(take(z0, z1)))) A__U71(tt, U12(and(z0, z1))) -> c32(A__LENGTH(a__U12(a__and(mark(z0), z1))), MARK(U12(and(z0, z1)))) A__U71(tt, U12(isNatIListKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatIListKind(z0))), MARK(U12(isNatIListKind(z0)))) A__U71(tt, U12(isNatKind(z0))) -> c32(A__LENGTH(a__U12(a__isNatKind(z0))), MARK(U12(isNatKind(z0)))) A__U71(tt, U12(cons(z0, z1))) -> c32(A__LENGTH(a__U12(cons(mark(z0), z1))), MARK(U12(cons(z0, z1)))) A__U71(tt, U12(0)) -> c32(A__LENGTH(a__U12(0)), MARK(U12(0))) A__U71(tt, U12(tt)) -> c32(A__LENGTH(a__U12(tt)), MARK(U12(tt))) A__U71(tt, U12(s(z0))) -> c32(A__LENGTH(a__U12(s(mark(z0)))), MARK(U12(s(z0)))) A__U71(tt, U12(nil)) -> c32(A__LENGTH(a__U12(nil)), MARK(U12(nil))) A__U71(tt, U12(x0)) -> c32(MARK(U12(x0))) K tuples:none Defined Rule Symbols: a__zeros, a__U11_2, a__U12_1, a__U21_2, a__U22_1, a__U31_2, a__U32_1, a__U41_3, a__U42_2, a__U43_1, a__U51_3, a__U52_2, a__U53_1, a__U61_3, a__U62_2, a__U63_1, a__U71_2, a__U81_1, a__U91_4, a__and_2, a__isNat_1, a__isNatIList_1, a__isNatIListKind_1, a__isNatKind_1, a__isNatList_1, a__length_1, a__take_2, mark_1 Defined Pair Symbols: A__U91_4, A__AND_2, A__ISNATKIND_1, MARK_1, A__U11_2, A__U21_2, A__U31_2, A__U42_2, A__U52_2, A__U62_2, A__U41_3, A__U51_3, A__U61_3, A__U71_2, A__ISNAT_1, A__ISNATILIST_1, A__ISNATILISTKIND_1, A__ISNATLIST_1, A__LENGTH_1, A__TAKE_2 Compound Symbols: c36_1, c38_1, c54_1, c55_1, c70_1, c73_1, c79_1, c93_1, c94_1, c95_1, c98_1, c2_1, c6_1, c10_1, c16_1, c22_1, c28_1, c69_1, c72_1, c75_1, c78_1, c82_1, c85_1, c88_1, c14_1, c20_1, c26_1, c32_2, c32_1, c41_2, c41_1, c42_2, c42_1, c44_2, c44_1, c46_3, c46_2, c50_2, c50_1, c51_2, c51_1, c58_3, c58_2, c59_3, c59_2, c62_4, c62_3, c62_2, c65_4, c65_3, c68_2, c68_1, c71_2, c71_1, c74_2, c74_1, c76_2, c76_1, c77_2, c77_1, c80_2, c80_1, c81_2, c81_1, c83_2, c83_1, c84_2, c84_1, c86_2, c86_1, c87_2, c87_1, c89_2, c89_1, c90_2, c90_1, c91_2, c91_1, c92_2, c92_1, c64_2, c64_1, c14_2, c20_2, c26_2